Question 60

What is the sum of the digits of the largest six-digit number divisible by 3, 4, 5 and 6?

Solution

As we know that the largest six-digit number is 999999.

The required number should be divisible by 3, 4, 5 and 6.

So the LCM of 3, 4, 5 and 6 is 60.

When 999999 is divided by 60, then the remainder will be 39.

$$999999=60\times16666+39$$

Required number = 999999-39 = 999960

the sum of the digits of the required number = 9+9+9+9+6+0 = 42

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