Question

Find the smallest square number which is divisible by each of the numbers 6,15,25

Answer 1

Answer:

First, let’s factor each of the proposed divisors into its prime factors:

8 = 2 * 2 * 2, 15 = 3 * 5, and 20 = 2 * 2 * 5. The least common multiple (LCM) is then

2 * 2 * 2 * 3 * 5 = 120. Now, any square that is evenly divisible by 8, 15, and 20 has

to be divisible by the LCM and any of its multiples. The multiple we want is the

smallest square, which can be generated by including an even number of each of

the factors in the prime factorization, namely 2 * 2 * 2 (* 2) *3 (* 3) *5 (* 5) or 120

(the LCM) * ( 2 * 3 * 5) = 120 * 30 = 3600.