Question 68

The largest three digit number that is exactly divisible by 6, 7 and 8 is:

Solution

6 = $$2\times3\times1$$

7 = $$7\times1$$

8 = $$2\times2\times2\times1$$

The LCM of 6, 7 and 8 is 168.

The largest three-digit number is 999.

The required number should be completely divisible by 168 which is the LCM of 6, 7 and 8.

So when we will divide 999 by 168, then the remainder will be 159.

Hence the required number = 999-159

= 840

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