Question

find the smallest square number which is divisible by each of the numbers 6 9 and 15

Answer 1

LCM of 6 3 into 2
9 3into3
15 5into 3
smallest number 3*2*3*3*5*3 = 810

Answer 2

Solution

This has to be done in two step, first find the smallest common multiple and then find the square number needed the least number divisible by each one of 6,9 and 15 is their LCM.

The LCM of 6,9 and 15 is

$2 \times 3 \times 3 \times 5 = 90$

Prime factorization of 90 of 90 equal to 2×3×3×5.

We

See the prime factors 2 and 5 are not in pairs thefore, 90 is not a perfect square.

In order to get a perfect square each factor of 90 must be paid so we need to make pairs of 2 and 5 ,therefore 90 should be multiplied by 2 ×5 , i.e.,10.

Hence, the required square number is 90×90=900