Question

If a and b are positive integers what is the smallest value of a b for which 2a 3b is divisible by 24?

Answer 1

The smallest value for
`\(a * b\)\\` making
`\(2^a * 3^b\)` divisible by 24 is 3, with a = 3 and b = 1. Thus, the answer is 3.

To find the smallest value of
`\(a * b\)` for which
`\(2^a * 3^b\)` is divisible by 24, we need to consider the prime factorization of 24.

The prime factorization of 24 is
`\(2^3 * 3^1\)`.

For
`\(2^a * 3^b\)` to be divisible by 24, a should be at least 3 and b should be at least 1 to include the prime factors of 24.

The smallest values satisfying this condition are a = 3 and b = 1.

So, the smallest value of
`\(a * b\)` is
`\(3 * 1 = 3\)`.

Therefore, the smallest value of
`\(a * b\)` for which
`\(2^a * 3^b\)` is divisible by 24 is 3.