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What is the smallest digit that replaces m, so that the number 54m61 is divisible by 9?

The smallest digit that replaces m is 2.

We know that a number N is divisible by 9 if the sum of its digits is divisible by 9.

Here, the sum of the known digits of 54m61 = 5 + 4 + m + 6 + 1 = 16 + m

Now, the number next to 16, which is divisible by 9 is 18.

Thus, if we replace the m by 2, the sum of digits will become 18 and the number becomes divisible by 9.

Hence, m is replaced by 2.