Question

Find the least square number exactly divisible by each one of the numbers 6, 9, 10, 15 and 20

Answer 1

First we find least number which is exactly divisible by numbers 6,9,15 and 20

For that we need to find LCM

6 = 2 * 3

9 = 3 * 3

15 = 3 * 5

20 = 2 * 2 * 5

LCM = 2 * 2 *  3  * 3 * 5 =  180

LCM = 2² * 3² * 5

To make it perfect square we need to multiply it by 5

= 2² * 3² * 5²

=  30²

= 900

900 is the least square number which is exactly divisible by each of the numbers 6,9,15 and 20

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