Question

my question is about factors and multiple chapter-

find the least number of 5 digits which is exactly divisible by 32,36,40,45&48?

Answer 1

Hi!

Here is the answer to your question.

The given numbers are 32, 36, 40, 45 and 48.

Prime factorization of 32 = 2 ×2 ×2 × 2 ×2

Prime factorization of 36 = 2 ×2 ×3 × 3

Prime factorization of 40 = 2 ×2 × 2 ×5

Prime factorization of 45 = 3 × 3 × 5

Prime factorization of 48 = 2 ×2 × 2 ×2 × 3

∴LCM of 32, 36, 40, 45 and 48 = 2 ×2 × 2 ×2 × 2 × 3 × 3 × 5 = 1440

1440 is the smallest number which is divisible by 32, 36, 40, 45 and 48.

Multiples of 1440 are 1440, 2880, 4320, 5760, 7200, 8640, 10080 …

Thus, the least five digit number exactly divisible by 32, 36, 40, 45 and 48 is 10080.

Cheers!