Question

least perfect square which is exactly divisible by 10,12,15,18

Answer 1

10=2×5

12=22×3

15=3×5

18=2×32

the least number that is divisible by 10,12,15,18 is the lcm(10,12,15,18)=22×32×5

a number is a square iff all its prime factors are raised to even powers.

Note that expect 5, all the other factors are already raised to even powers,

In order to make this product a square it should be multiplied by an odd power of 5

And to make the square the least,multiply the product by 51(because 1 is the least positive integer),and then it becomes 22×32×52=900