Find the least square number which is exactly divisible by each of the

1.	Find the least square number which is exactly divisible by each of the numbers 8, 12, 15 and 20.
Answer» We know that, The smallest number that is divisible by each o0f these numbers is their L.C.M So, L.C.M of 8, 12, 15, 20 = 120 Resolving into prime factors, we get 120 = 2 × 2 × 2 × 3 × 5 So, for making it a perfect square we have to multiply it by 2 × 3 × 5 = 30 Multiplying the number by 30, we get Required number = 120 × 30 = 3600

Find the least square number which is exactly divisible by each of the numbers 8, 12, 15 and 20.

Answer»

We know that,

The smallest number that is divisible by each o0f these numbers is their L.C.M

So,

L.C.M of 8, 12, 15, 20 = 120

Resolving into prime factors, we get

120 = 2 × 2 × 2 × 3 × 5

So, for making it a perfect square we have to multiply it by 2 × 3 × 5 = 30

Multiplying the number by 30, we get

Required number = 120 × 30

= 3600