Question

LCM of three natural numbers 150,144 and x is 10800. How many values of x are possible ?

Answer 1

10800 = 2^4 x 3^3 x 5^2

150 = 2 x 3 x 5^2

144 = 2^4 x 3^2

LCM of 144 and 150 = 2^4 x 3^2 x 5^2 = 3600

If the LCM of 144, 150 and x has to be 10,800, we conclude that

x must contain 3^3 and any combination of powers of 2 ^(<=4) and 5 ^ (<=2)

Hence x shall have the following values:

3^3 = 27

27 x 2 = 54

27 x 2^2 = 108

27 x 2^3 = 216