Let x be the least number divisible by 24, 30, 36, 45 and 50 and x is also a perfect square

Let x be the least number divisible by 24, 30, 36, 45 and 50 and x is also a perfect square. What is the remainder when x is divided by 233?

(a) 55

(b) 105

(c) 170

(d) 103

Sol:

L.C.M of (24, 30, 36, 45, 50) = 1800 = 900× 2

For a perfect square = 900 × 2 × 2 = 3600

Remainder=3600/233=15 105/233