Find the smallest perfect square number which is exactly divisible by 12, 15, and 20
A)180
B)360
C)900
D)32400

Question

Quizplus · Accepted Answer

First find LCM which is exactly divisible by 12, 15, and 20
12 = 2x2x3x3
15= 3x5
20= 2x2x5
LCM = 2x2x3x3x5. In the LCM 2 and 3 have their pairs, but 5 are alone. Pairs are perfect squares. So we have to multiply LCM by 5 to make it perfect square.
2x2x3x3x5x5 =900 is the smallest perfect square number
Key takeaway: The Least Common Multiple (LCM) is the smallest number that is a multiple of two or more numbers. Write each number as products of their prime factors.

Find the Smallest Perfect Square Number Which Is Exactly Divisible