Divide the LCM of 20,30 and40 by their HCF

Answer 1

To find the LCM (Least Common Multiple) of 20, 30, and 40, we need to find the smallest number that is divisible by all three numbers.

Prime factorization of 20: 2^2 * 5
Prime factorization of 30: 2 * 3 * 5
Prime factorization of 40: 2^3 * 5

The LCM is found by taking the highest powers of all prime factors that appear in the prime factorizations of the numbers.
So, LCM of 20, 30, and 40 = 2^3 * 3 * 5 = 120

Now, let's find the HCF (Highest Common Factor) of 20, 30, and 40. It is the largest number that divides all three numbers.

The common prime factors of 20, 30, and 40 are 2 and 5.
So, HCF of 20, 30, and 40 = 2 * 5 = 10

Dividing the LCM by the HCF:
120 ÷ 10 = 12

Therefore, the LCM of 20, 30, and 40 divided by their HCF is 12.