Question

Determine the largest three digit number exactly divisible by 8 10 and 12

Answer 1

8=2×2×2=2^3
10=2×5
12=2×2×3=2^2×3

LCM(8,10,12)=Product of greatest power of each factor
=2^3×3×5
=120

The number which divisible by 8,10 and 12 is also divisible by 120

Largest three dugit number is 999

On dividing 999 by 120 we get:-

39 as remainder

Hence,required number=999-39
=960 Ans.