Question

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

Answer 1

Find the LCM of given numbers. Square it to get the answer.

8 = 2^3

12 = 2^2 * 3

15 = 3 * 5

20 = 2^2 * 5

LCM = 2^3 * 3 * 5

= 120

Answer = LCM^2

= 14400

It is not given in the options.

Edit :

I made a mistake. Thank you for pointing it out Vignesh Sriram .

The correct method would be

Find the LCM of the given numbers(which is 120 in this case)

Find the prime factorisation of the LCM

(120 = 2^3 *3 *5)

Now multiply the LCM by prime factors so that all the prime factors will have even multiplicities.

Answer = (2^3 * 3* 5) * (2*3*5)

= 2^4 * 3^2 * 5^2

= 3600