Question

Find the least number of Five digit that is exactly divisible by 16 18 24 and 30

Answer 1

16=2×2×2×2 =2^4
18=2×3×3 =2×3^2
24=2×2×2×3 =2^3×3
30=2×3×5

LCM(16,18,24,30)=Product of highest power of each factor.
=2^4×3^2×5
=720

Any number divisible by 16,18,24 and 30 must be divisible by 720.

Smallest five digit number=10,000

On dividing 10,000 by 720 we get 640 as remainder.

Required number=10,000+(720-640)
=10,000+80
=10,080 Ans.