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