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Question

Determine the largest 3-digit number which is exactly divisible by 8,10 and 12.


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Solution

STEP 1 : Finding the L.C.M. of 8,10 and 12 by division method

Using the division method we find the LCM of 8,10 and 12.

L.C.M. of 8,10 and 12 =2×2×2×3×5=23×3×5

L.C.M. of 8,10 and 12 =8×3×5=120

STEP 2 : Finding the largest 3-digit number which is multiple of 120

We know that largest 3-digit number is 999

Dividing 999 by 120 we get

999=120×8+39

If we subtract the remainder from 999 we get the largest 3-digit number which is multiple of 120

120×8=999-39=960

i.e. 960 is the largest 3-digit number which is multiple of 120.

Hence, the largest 3-digit number which is exactly divisible by 8,10 and 12 is 960.


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