Question

Find the smallest square number divisible by each one of the numbers 8, 9 and 10.

Answer 1

Given: The least-square number which is exactly divisible by 8, 9 and 10 is equal to L.C.M. of 8, 9 and 10.

2	8, 9, 10
2	4, 9, 5
2	2, 9, 5
3	1, 9, 5
3	1, 3, 5
5	1, 1, 5
	1, 1, 1

Hence, their L.C.M. is 2 × 2 × 2 × 3 × 3 × 5 = 360

As we see, (2 × 2) × 2 × (3 × 3) × 5

i.e. 2 and 5 is not able to make their pair.

Hence, to make it perfect square, it must be multiplied with 2 × 5 = 10

As, 360 × 10 = 3600

Hence, 3600 is least square number which is exactly divisible by 8, 9 and 10.