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