Question

If two positive integers m and n are expressible in the form m = a²b³ and n = a³b², where a, b are prime numbers, then HCF (m, n) = ______ and LCM (a, b) = ______.

Answer 1

If two positive integers m and n are expressible in the form m = a²b³ and n = a³b², where a, b are prime numbers, then HCF (m, n) = a²b² and LCM (a, b) = a³b³.

Explanation:

For each prime the HCF takes the minimum exponent and the LCM takes the maximum exponent.

For a: min(2, 3) = 2, max(2, 3) = 3.

For b: min(3, 2) = 2, max(3, 2) = 3.

So HCF(m, n) = a²b² and LCM(m, n) = a³b³.