FPB, KPK, Soal Cerita

1. FPB dari 24, 36, dan 42 adalah….

24

8

6

3

The given question asks for the greatest common divisor (FPB) of the numbers 24, 36, and 42. To find the FPB, we need to find the largest number that can divide all three numbers without leaving a remainder. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. The largest number that is common to all three sets of factors is 6. Therefore, the FPB of 24, 36, and 42 is 6.

Explanation

The given question asks for the greatest common divisor (FPB) of the numbers 24, 36, and 42. To find the FPB, we need to find the largest number that can divide all three numbers without leaving a remainder. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. The largest number that is common to all three sets of factors is 6. Therefore, the FPB of 24, 36, and 42 is 6.

2. Faktor persekutuan terbesar (FPB) dari 16, 24, dan 32 adalah….

4

6

8

12

The greatest common factor (GCF) or highest common factor (HCF) is the largest number that divides evenly into all given numbers. In this case, the numbers given are 16, 24, and 32. To find the GCF, we need to determine the factors of each number. The factors of 16 are 1, 2, 4, 8, and 16. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 32 are 1, 2, 4, 8, 16, and 32. The largest number that appears in all three lists is 8, so it is the GCF or FPB of 16, 24, and 32.

Explanation

The greatest common factor (GCF) or highest common factor (HCF) is the largest number that divides evenly into all given numbers. In this case, the numbers given are 16, 24, and 32. To find the GCF, we need to determine the factors of each number. The factors of 16 are 1, 2, 4, 8, and 16. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 32 are 1, 2, 4, 8, 16, and 32. The largest number that appears in all three lists is 8, so it is the GCF or FPB of 16, 24, and 32.

3. Bu Lastri mempunyai 36 buah mangga, 60 buah jeruk, dan 72 buah salak. Buah-buah tersebut dikemas untuk dibagikan kepada tetangga. Setiap kemasan berisi buah dengan jumlah dan jenis berbeda yang sama banyak. Bu Lastri paling banyak dapat membuat……..kemasan

6

12

15

30

Bu Lastri memiliki 36 mangga, 60 jeruk, dan 72 salak. Untuk membuat kemasan dengan jumlah dan jenis buah yang sama banyak, kita perlu mencari faktor persekutuan terbesar (FPB) dari 36, 60, dan 72. FPB dari 36, 60, dan 72 adalah 12. Oleh karena itu, Bu Lastri dapat membuat 12 kemasan dengan jumlah dan jenis buah yang sama banyak.

Explanation

Bu Lastri memiliki 36 mangga, 60 jeruk, dan 72 salak. Untuk membuat kemasan dengan jumlah dan jenis buah yang sama banyak, kita perlu mencari faktor persekutuan terbesar (FPB) dari 36, 60, dan 72. FPB dari 36, 60, dan 72 adalah 12. Oleh karena itu, Bu Lastri dapat membuat 12 kemasan dengan jumlah dan jenis buah yang sama banyak.

4. Kelipatan persekutuan terkecil (KPK) dari 15, 20, dan 60 adalah….

5

15

30

60

The least common multiple (LCM) of 15, 20, and 60 is the smallest number that is divisible by all three numbers. To find the LCM, we can list the multiples of each number until we find a common multiple. The multiples of 15 are 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, etc. The multiples of 20 are 20, 40, 60, 80, 100, 120, 140, 160, etc. The multiples of 60 are 60, 120, 180, 240, 300, etc. The smallest number that appears in all three lists is 60, so the LCM of 15, 20, and 60 is 60.

Explanation

The least common multiple (LCM) of 15, 20, and 60 is the smallest number that is divisible by all three numbers. To find the LCM, we can list the multiples of each number until we find a common multiple. The multiples of 15 are 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, etc. The multiples of 20 are 20, 40, 60, 80, 100, 120, 140, 160, etc. The multiples of 60 are 60, 120, 180, 240, 300, etc. The smallest number that appears in all three lists is 60, so the LCM of 15, 20, and 60 is 60.

5. Kelipatan persekutuan terkecil (KPK) dari 56, 63, dan 84 adalah….

168

252

336

504

The least common multiple (LCM) of three numbers is the smallest number that is divisible by all three numbers. To find the LCM of 56, 63, and 84, we can list the multiples of each number and find the smallest number that appears in all three lists. The multiples of 56 are 56, 112, 168, 224, 280, 336, 392, 448, 504, 560, 616, 672, 728, 784, 840, 896, 952, 1008, 1064, 1120. The multiples of 63 are 63, 126, 189, 252, 315, 378, 441, 504, 567, 630, 693, 756, 819, 882, 945, 1008. The multiples of 84 are 84, 168, 252, 336, 420, 504, 588, 672, 756, 840, 924, 1008. The smallest number that appears in all three lists is 504, so the LCM of 56, 63, and 84 is 504.

Explanation

The least common multiple (LCM) of three numbers is the smallest number that is divisible by all three numbers. To find the LCM of 56, 63, and 84, we can list the multiples of each number and find the smallest number that appears in all three lists. The multiples of 56 are 56, 112, 168, 224, 280, 336, 392, 448, 504, 560, 616, 672, 728, 784, 840, 896, 952, 1008, 1064, 1120. The multiples of 63 are 63, 126, 189, 252, 315, 378, 441, 504, 567, 630, 693, 756, 819, 882, 945, 1008. The multiples of 84 are 84, 168, 252, 336, 420, 504, 588, 672, 756, 840, 924, 1008. The smallest number that appears in all three lists is 504, so the LCM of 56, 63, and 84 is 504.

6. Kelipatan persekutuan terkecil (KPK) dari 42, 56, dan 63 adalah….

168

252

405

504

The question asks for the least common multiple (KPK) of 42, 56, and 63. To find the KPK, we need to find the smallest number that is divisible by all three given numbers. The prime factorization of 42 is 2 x 3 x 7, the prime factorization of 56 is 2 x 2 x 2 x 7, and the prime factorization of 63 is 3 x 3 x 7. To find the KPK, we take the highest power of each prime factor that appears in any of the numbers. So, the KPK of 42, 56, and 63 is 2 x 2 x 2 x 3 x 3 x 7, which equals 504.

Explanation

The question asks for the least common multiple (KPK) of 42, 56, and 63. To find the KPK, we need to find the smallest number that is divisible by all three given numbers. The prime factorization of 42 is 2 x 3 x 7, the prime factorization of 56 is 2 x 2 x 2 x 7, and the prime factorization of 63 is 3 x 3 x 7. To find the KPK, we take the highest power of each prime factor that appears in any of the numbers. So, the KPK of 42, 56, and 63 is 2 x 2 x 2 x 3 x 3 x 7, which equals 504.

7. Bus X berangkat dari terminal setiap 30 menit sekali, sedangkan bus Y setiap 45 menit sekali. Jika kedua bus berangkat bersama pada pukul 06.45, pada pukul berapakah kedua bus akan berangkat bersama lagi?

Pukul 08.15

Pukul 08.00

Pukul 07.30

Pukul 07.15

Bus X berangkat setiap 30 menit sekali dan bus Y berangkat setiap 45 menit sekali. Dalam waktu 1 jam (60 menit), bus X berangkat 2 kali (pada pukul 07.15 dan 07.45) dan bus Y berangkat 1 kali (pada pukul 07.30). Oleh karena itu, waktu berikutnya ketika kedua bus akan berangkat bersama lagi adalah setelah 1 jam (60 menit) dari pukul 07.30, yaitu pada pukul 08.30. Namun, karena bus X berangkat setiap 30 menit sekali, maka waktu berikutnya kedua bus akan berangkat bersama adalah setelah 45 menit dari pukul 08.30. Jadi, kedua bus akan berangkat bersama lagi pada pukul 08.15.

Explanation

Bus X berangkat setiap 30 menit sekali dan bus Y berangkat setiap 45 menit sekali. Dalam waktu 1 jam (60 menit), bus X berangkat 2 kali (pada pukul 07.15 dan 07.45) dan bus Y berangkat 1 kali (pada pukul 07.30). Oleh karena itu, waktu berikutnya ketika kedua bus akan berangkat bersama lagi adalah setelah 1 jam (60 menit) dari pukul 07.30, yaitu pada pukul 08.30. Namun, karena bus X berangkat setiap 30 menit sekali, maka waktu berikutnya kedua bus akan berangkat bersama adalah setelah 45 menit dari pukul 08.30. Jadi, kedua bus akan berangkat bersama lagi pada pukul 08.15.

8. Ibnu berenang setiap 3 hari, Ishak berenang setiap 4 hari, dan Muis berenang setiap 5 hari. Jika pada tanggal 1 Maret 2017 mereka berenang bersama, maka mereka akan berenang bersama kembali pada tanggal….

29 April 2017

30 April 2017

1 Mei 2017

2 Mei 2017

Ibnu, Ishak, and Muis swim together every 3, 4, and 5 days respectively. To find the next date they swim together, we need to find the least common multiple (LCM) of 3, 4, and 5. The LCM of 3, 4, and 5 is 60. Therefore, they will swim together again after 60 days. Since they swam together on March 1, 2017, we need to add 60 days to that date. April has 30 days, so the next date they swim together will be on April 30, 2017.

Explanation

Ibnu, Ishak, and Muis swim together every 3, 4, and 5 days respectively. To find the next date they swim together, we need to find the least common multiple (LCM) of 3, 4, and 5. The LCM of 3, 4, and 5 is 60. Therefore, they will swim together again after 60 days. Since they swam together on March 1, 2017, we need to add 60 days to that date. April has 30 days, so the next date they swim together will be on April 30, 2017.

9. Faktor persekutuan terbesar (FPB) dari 28, 42, dan 76 adalah….

14

7

4

2

The greatest common factor (GCF) is the largest number that divides evenly into all given numbers. To find the GCF of 28, 42, and 76, we can list the factors of each number and find the largest number that appears in all three lists. The factors of 28 are 1, 2, 4, 7, 14, and 28. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. The factors of 76 are 1, 2, 4, 19, 38, and 76. The largest number that appears in all three lists is 2, so the correct answer is 2.

Explanation

The greatest common factor (GCF) is the largest number that divides evenly into all given numbers. To find the GCF of 28, 42, and 76, we can list the factors of each number and find the largest number that appears in all three lists. The factors of 28 are 1, 2, 4, 7, 14, and 28. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. The factors of 76 are 1, 2, 4, 19, 38, and 76. The largest number that appears in all three lists is 2, so the correct answer is 2.

10. Tini membersihkan akuarium setiap 6 hari sekali, sedangkan Tina setiap 5 hari sekali. Pada tanggal 5 April 2017 mereka bersama-sama membersihkan akuarium. Mereka membersihkan akuarium bersama-sama lagi untuk kedua kalinya pada tanggal……

25 April 2017

30 April 2017

4 Mei 2017

5 Mei 2017

Tini membersihkan akuarium setiap 6 hari sekali, sedangkan Tina setiap 5 hari sekali. Pada tanggal 5 April 2017 mereka bersama-sama membersihkan akuarium. Jarak antara tanggal 5 April dan 5 Mei adalah 30 hari. Karena Tini membersihkan akuarium setiap 6 hari sekali, maka dia akan membersihkan akuarium pada tanggal 11 April, 17 April, 23 April, dan 29 April. Sementara itu, Tina membersihkan akuarium setiap 5 hari sekali, jadi dia akan membersihkan akuarium pada tanggal 10 April, 15 April, 20 April, 25 April, dan 30 April. Jadi, mereka akan membersihkan akuarium bersama-sama lagi untuk kedua kalinya pada tanggal 5 Mei 2017.

Explanation

Tini membersihkan akuarium setiap 6 hari sekali, sedangkan Tina setiap 5 hari sekali. Pada tanggal 5 April 2017 mereka bersama-sama membersihkan akuarium. Jarak antara tanggal 5 April dan 5 Mei adalah 30 hari. Karena Tini membersihkan akuarium setiap 6 hari sekali, maka dia akan membersihkan akuarium pada tanggal 11 April, 17 April, 23 April, dan 29 April. Sementara itu, Tina membersihkan akuarium setiap 5 hari sekali, jadi dia akan membersihkan akuarium pada tanggal 10 April, 15 April, 20 April, 25 April, dan 30 April. Jadi, mereka akan membersihkan akuarium bersama-sama lagi untuk kedua kalinya pada tanggal 5 Mei 2017.

Fpb, Kpk, Soal Cerita