Question

The least perfect square number which is divisible by 8, 15, 20, 22 is

• A. 435600
• B. 43560
• C. 39600
• D. None

Answer 1

The correct option is A 435600

Lets first analyze the factors of $8,15,20,22$
$8=2^3$
$15=3\ast 5$
$20=4\ast 5$
$22=2\ast 11$
Perfect square can only be possible, if all the prime numbers are present even number of times and greater than or equal to the number of times they are present in the given four numbers.
i.e $2^4\ast 3^2\ast 5^2\ast {11}^2$
$=16\ast 9\ast 25\ast 121$
$=435600$
Option A