Question

Find the smallest perfect square divisible by 6,8,10,12

Answer 1

Answer:

3600 is a perfect square

Step-by-step explanation:

Take LCM of (6,8,12 and 10) = 120

Resolving 120 into prime factors, we get

120 = 2*2*2*3*5

Here 2 is grouped in pairs of equal factors. But 2, 3 and 5 are not grouping in pairs of equal factors.

Let us multiply 2, 3 and 5 , we get a grouped in pairs of equal factors.

120*2*3*5 = 2*2*2*2*3*3*5*5

3600 = 2*2*2*2*3*3*5*5

Now 3600 is perfect square that is divisible by 6, 8, 12, 10

Answer 2

Answer:

Take LCM of (6,8,12 and 10) = 120, on solving 120 in prime factors, we get 120 = 2*2*2*3*5. But 2, 3 and 5 are not grouping pairs of identical factors. Let us multiply 2, 3 and 5, we get a group in pairs of identical factors. 120*2*3*5 = 2*2*2*2*3*3*5*5 3600 = 2*2*2*2*3*3*5*5 Now 3600 is a perfect square which is divisible by 6 , 8, 12, 10