Question

Find the number neaest to 1000 but greater that 1000,which is exactly divisible by 8,12,18

Answer 1

8=2×2×2 =2^3
12=2×2×3=2^2×3
18=2×3×3=2×3^2

LCM(8,12,18)=product of highest power of each factor.
=2^3×3^2
=72

Any number divisble by 8,12 and 18 must be divisible by 72

On dividing 1,000 by 72 we get 64 as remainder.

Hence the required number=1,000+(72-64)
=1,000+8
=1,008 Ans.