Question

What is the lowest common multiple of 36 and 135 that is also a square numbe

Answer 1

36 = 2 × 2 × 3 × 3

135 = 3 × 3 × 3 × 5

LCM = 2 × 2 × 3 × 3 × 3 × 5 = 2²3³5

Find the smallest natural numbers a, b, and c such that (2²a)(3³b)(5c) is a perfect square.

a = 1, b = 3, c = 5

So we have 2²3⁴5² = 4(81)(25) = 8,100.