HCF And LCM Quiz

The highest common factor (HCF) of two numbers is the largest number that divides both of them without leaving a remainder. In this case, the factors of 6 are 1, 2, 3, and 6, while the factors of 15 are 1, 3, 5, and 15. The largest number that appears in both lists is 3, so it is the HCF of 6 and 15.

The highest common factor (HCF) is the largest number that divides both 15 and 50 without leaving a remainder. To find the HCF, we can list the factors of each number. The factors of 15 are 1, 3, 5, and 15. The factors of 50 are 1, 2, 5, 10, 25, and 50. The largest number that appears in both lists is 5, so the HCF of 15 and 50 is 5.

LCM stands for Least Common Multiple. The LCM is the smallest multiple that two or more numbers have in common. It is used to find the smallest common multiple when dealing with fractions or finding a common denominator.

The HCF (Highest Common Factor) of 12 and 66 is 6. HCF is the largest number that divides both given numbers evenly. In this case, 6 is the largest number that can divide both 12 and 66 without leaving any remainder. Therefore, 6 is the correct answer.

The LCM (Least Common Multiple) is the smallest number that is a multiple of both 8 and 10. To find it, we can list the multiples of 8 and 10 and find the smallest number that appears in both lists. The multiples of 8 are 8, 16, 24, 32, 40, ... and the multiples of 10 are 10, 20, 30, 40, .... The smallest number that appears in both lists is 40, so the LCM of 8 and 10 is 40.

The LCM (Least Common Multiple) of two numbers is the smallest number that is divisible by both of them without leaving a remainder. To find the LCM of 24 and 36, we can list the multiples of both numbers and find the smallest common multiple. The multiples of 24 are 24, 48, 72, 96, 120, 144, ... and the multiples of 36 are 36, 72, 108, 144, 180, 216, ... The smallest common multiple is 72, which means that 72 is the LCM of 24 and 36.

Prime Factorization:

44 = 2 × 2 × 11

62 = 2 × 31

Identify the highest powers of all prime factors:

The prime factors are 2, 11, and 31.

The highest powers of these factors are:

2^2 (from 44)

11 (from 44)

31 (from 62)

Multiply the highest powers of all prime factors:

LCM = 2^2 × 11 × 31

LCM = 4 × 11 × 31 = 1364

To find the least common multiple (LCM) of 32 and 72, we can use the following steps:

Prime Factorization: Find the prime factors of each number:

32 = 2 x 2 x 2 x 2 x 2 = 2^5

72 = 2 x 2 x 2 x 3 x 3 = 2^3 x 3^2

Identify Common and Uncommon Factors: Both numbers have 2 as a common prime factor. 32 has more 2's, and 72 has 3's.

Calculate the LCM: Take the highest power of each prime factor present in the factorizations: 2^5 x 3^2 = 32 x 9 = 288

Therefore, the LCM of 32 and 72 is 288.

To find the Highest Common Factor (HCF) of 39 and 52, follow these steps:

Prime Factorization:

39 = 3 × 13

52 = 2 × 2 × 13

Identify the common factors:

Both 39 and 52 have the common factor of 13.

Therefore, the HCF of 39 and 52 is 13.

HCF stands for Highest Common Factor. It is a mathematical term used to denote the largest number that divides two or more numbers without leaving a remainder. It is also known as the Greatest Common Divisor (GCD).