**Question:**

Find the least square number, exactly divisible by each one of the numbers:

(i) 6, 9, 15 and 20

(ii) 8, 12, 15 and 20

**Solution:**

(i) The smallest number divisible by 6, 9, 15 and 20 is their L.C.M., which is equal to 60.

Factorising 60 into its prime factors:

60 = 2 x 2 x 3 x 5

Grouping them into pairs of equal factors:

60 = (2 x 2) x 3 x 5

The factors 3 and 5 are not paired. To make 60 a perfect square, we have to multiply it by 3 x 5, i.e . by15.

The perfect square is 60 x 15, which is equal to 900

(i) The smallest number divisible by 8, 12, 15 and 20 is their L.C.M., which is equal to 120.

Factorising 120 into its prime factors:

120 = 2 x 2 x 2 x 3 x 5

Grouping them into pairs of equal factors:

120 = (2 x 2) x 2 x 3 x 5

The factors 2, 3 and 5 are not paired. To make 120 into a perfect square, we have to multiply it by 2 x 3 x 5, i.e. by 30.

The perfect square is 120 x 30, which is equal to 3600.