Question

what is the smallest perfect square that can be divided by 15 and 21

Answer 1

8 = 2^3
12 = 2^2 * 3
15 = 3 * 5
20 = 2^2 * 5

LCM = 2^3 * 3 * 5
= 120
Answer = LCM^2
= 14400

Answer 2

Answer: 11025

Step-by-step explanation:

L.C.M. of 15 and 21 is 105.

so if we want to find a perfect square it must be a multipe of 105.

let that number is 105x

factor of 105x is

105x = 3*5*7*x

as we know for being a number to square it must have pair of prime numbers in its factor. it it have pair then it is called a perfect square and if not then it is not a perfect square.

so there must be a pair of 3, 5, 7.

so the value of x is 3*5*7 = 105

so formed umber = 11025