Question

Q.7 Find the least square number which is exactly divisible by each of the numbers
8, 12, 15 ,20 ​

Answer 1

First let's 8, 12, 15, and 20

8 = 2 × 2× 2

12 = 2 × 2 × 3

15 = 3 × 5

20 = 2 × 2 × 5

So, the LCM is 2 × 2 × 2 × 3 × 5 = 120

Here is 2, 3, and 5 are not in pairs, we need to in pairs for smallest square number.

120 × 2 × 3 × 5 = 120 × 30 = 3600

Hence, the number is 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 = 3600

Answer 2

first we need to find the LCM of the given numbers i.e. 8, 12, 15 and 20

2*2*2*5*3=120

Then

as 2, 3, 5 are not in pairs, we need to multiply the LCM with 2*5*3=30

so,

least perfect square number which is divisible by each of numbers 8 12 15 and 20


=120*30=3600