Question

Find the smallest 4 digit number that is exactly divisible by 36,40,45

Answer 1

Here you go

The smallest 4-digit number which is divisible by 36, 40 and 45.

36=2x2x3x3 = 2^2 x 3^2

40=2x2x2x5 = 2^3 x 5

45=3x3x5 = 3^2 x 5

LCM (36, 40, 45 ) =  2^3 x 3^2 x 5 = 8 x 9 x 5 =40 x 9 =360

 ∴  Required smallest 4-digit number which is divisible by 36, 40 and 45 is =  3 x 360 = 1080