Question

M is the largest 4 digit number, which when divided by 4, 5, 6 and 7 leaves remainder as 2, 3, 4, and 5 respectively. What will be the remainder when M is divided by 9

Answer 1

You find the LCM of 3, 5, 7 and 9, which is 315. Then you find the largest multiple of 315 such that it’s 9999 or less. This is 31. Multiply 315 by 31 to come to 9765. Since the remainders are 2 less than the respective numbers, subtract 2 from it to arrive at 9763. Now add 315 (LCM) to it to see if it’s still under 5 digits. In this case it’s not so now 9763 is your answer.

Answer 2

The remainder when M is divided by 9 is 1.

Given:

M is the largest 4-digit number, which when divided by 4, 5, 6, and 7 leave the remainder as 2, 3, 4, and 5.

To Find:

The remainder when M is divided by 9.

Solution:

Here, it is given that the remainder of the division of M by 4, 5, 6, and 7 is 2, 3, 4, and 5.

So, the LCM of 4, 5, 6, and 7 = 420.

Let's suppose that the largest 4-digit number is 9999.

now, divide 9999 by the LCM of 4, 5, 6, and 7 which is 420.

we get, the remainder as 339.

now, subtract 9999 from 339, then we get 9660.

here, the difference between divisor and remainder (4-2), (5-3), (6-4), and (7-5) is 2.

now, subtract 9660 from 2, then we get, 9660 - 2 = 9658 = M.

let's divide 9658 by 9, then we get, the remainder as 1.

Hence, the remainder when M is divided by 9 is 1.

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