HCF And LCM Quiz Questions For Class 5

1. The common factor between the numerator and denominator of 6/15 is ______

3

2

5

4

The common factor between the numerator and denominator of 6/15 is 3. This is because both 6 and 15 can be divided evenly by 3.

Explanation

The common factor between the numerator and denominator of 6/15 is 3. This is because both 6 and 15 can be divided evenly by 3.

2. The L.C.M of 3, 6, and 9 is

6

9

15

18

The LCM (Least Common Multiple) of 3, 6, and 9 can be found by listing the multiples of each number and finding the smallest number that appears in all three lists. The multiples of 3 are 3, 6, 9, 12, 15, 18, ... The multiples of 6 are 6, 12, 18, 24, 30, ... The multiples of 9 are 9, 18, 27, 36, ... The smallest number that appears in all three lists is 18, so the LCM of 3, 6, and 9 is 18.

Explanation

The LCM (Least Common Multiple) of 3, 6, and 9 can be found by listing the multiples of each number and finding the smallest number that appears in all three lists. The multiples of 3 are 3, 6, 9, 12, 15, 18, ... The multiples of 6 are 6, 12, 18, 24, 30, ... The multiples of 9 are 9, 18, 27, 36, ... The smallest number that appears in all three lists is 18, so the LCM of 3, 6, and 9 is 18.

3. The H.C.F of 8 and 12 is

4

6

8

12

The highest common factor (H.C.F) of two numbers is the largest number that divides both of them without leaving a remainder. In this case, the factors of 8 are 1, 2, 4, and 8, while the factors of 12 are 1, 2, 3, 4, 6, and 12. The largest number that divides both 8 and 12 is 4, making it the H.C.F.

Explanation

The highest common factor (H.C.F) of two numbers is the largest number that divides both of them without leaving a remainder. In this case, the factors of 8 are 1, 2, 4, and 8, while the factors of 12 are 1, 2, 3, 4, 6, and 12. The largest number that divides both 8 and 12 is 4, making it the H.C.F.

4. The H.C.F. of 7, 11, and 13 is __________

7

77

1

101

The H.C.F. (Highest Common Factor) of 7, 11, and 13 is 1. This is because 1 is the only positive integer that divides all three numbers without leaving a remainder.

Explanation

The H.C.F. (Highest Common Factor) of 7, 11, and 13 is 1. This is because 1 is the only positive integer that divides all three numbers without leaving a remainder.

5. The smallest among all the common multiples of the given numbers is called their __________

H.C.F.

L.C.M.

Product

Multiple

The smallest among all the common multiples of the given numbers is called their L.C.M. This is because the L.C.M. (Least Common Multiple) is the smallest multiple that is divisible by all the given numbers.

Explanation

The smallest among all the common multiples of the given numbers is called their L.C.M. This is because the L.C.M. (Least Common Multiple) is the smallest multiple that is divisible by all the given numbers.

6. The L.C.M. of 4, 8, and 16 is _________

2

4

1

16

The L.C.M. (Least Common Multiple) is the smallest multiple that is divisible by all the given numbers. In this case, the L.C.M. of 4, 8, and 16 is 16 because it is the smallest number that is divisible by all three numbers without leaving a remainder. Therefore, the correct answer is 16.

Explanation

The L.C.M. (Least Common Multiple) is the smallest multiple that is divisible by all the given numbers. In this case, the L.C.M. of 4, 8, and 16 is 16 because it is the smallest number that is divisible by all three numbers without leaving a remainder. Therefore, the correct answer is 16.

7. The L.C.M of 5, 10, and 18 is

80

85

90

180

To find the least common multiple (LCM) of 5, 10, and 18, we need to determine the smallest number that is divisible by all three numbers. The prime factors of 5 are 5, the prime factors of 10 are 2 and 5, and the prime factors of 18 are 2 and 3. To find the LCM, we take the highest power of each prime factor that appears in any of the numbers. In this case, the LCM would be 2^1 * 3^1 * 5^1 = 2 * 3 * 5 = 30. Therefore, the given answer of 90 is incorrect.

Explanation

To find the least common multiple (LCM) of 5, 10, and 18, we need to determine the smallest number that is divisible by all three numbers. The prime factors of 5 are 5, the prime factors of 10 are 2 and 5, and the prime factors of 18 are 2 and 3. To find the LCM, we take the highest power of each prime factor that appears in any of the numbers. In this case, the LCM would be 2^1 * 3^1 * 5^1 = 2 * 3 * 5 = 30. Therefore, the given answer of 90 is incorrect.

8. The L.C.M. of two or more mutually prime numbers is given by their ________

Product

1

H.C.F.

Biggest number

The L.C.M. (Least Common Multiple) of two or more mutually prime numbers is given by their product. This means that when two or more numbers are mutually prime, their L.C.M. will be equal to the product of those numbers.

Explanation

The L.C.M. (Least Common Multiple) of two or more mutually prime numbers is given by their product. This means that when two or more numbers are mutually prime, their L.C.M. will be equal to the product of those numbers.

9. All the given numbers are divisible by their ________

L.C.M.

!

H.C.F.

Product

The correct answer is H.C.F. (Highest Common Factor). The question suggests that all the given numbers are divisible by their H.C.F. This means that the highest factor that divides each of the given numbers without leaving a remainder is the H.C.F. Therefore, the H.C.F. is the correct answer.

Explanation

The correct answer is H.C.F. (Highest Common Factor). The question suggests that all the given numbers are divisible by their H.C.F. This means that the highest factor that divides each of the given numbers without leaving a remainder is the H.C.F. Therefore, the H.C.F. is the correct answer.

10. The H.C.F. of two or more mutually prime numbers is _____

L.C.M.

10

Product

1

When two or more numbers are mutually prime, it means that they do not have any common factors other than 1. In such cases, the highest common factor (H.C.F.) of these numbers will always be 1. Therefore, the H.C.F. of mutually prime numbers is 1.

Explanation

When two or more numbers are mutually prime, it means that they do not have any common factors other than 1. In such cases, the highest common factor (H.C.F.) of these numbers will always be 1. Therefore, the H.C.F. of mutually prime numbers is 1.