The least number when divided by 36,49 and 64 leaves remainder 25, 37 and 53 respectively is?

# The least number when divided by 36,49 and 64 leaves remainder 25, 37 and 53 respectively is?

1. A
515
2. B
535
3. C
576
4. D
585

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### Solution:

Concept- You can see that we need to find the smallest number that, when  divided by 36, 48, 64,  the remainder  is exactly 11 less than the divisor. This is how we  find  L.C.M. Numbers 36, 48, and 64, and subtract 11 from them.
Given least number when divided by 36,49 and 64 leaves remainder 25, 37 and 53 respectively
From this we conclude that the required division should be 11 less than the exact multiple of the divisor.
For the three numbers 36, 48 and 64, L.C.M. You can use it to determine the least frequent multiple.
Prime Factorization of 36, 48 and 64
For each prime factor, find where it occurs most often as a factor and write the number to a new list 2, 2, 2, 2, 2, 3, 3
By multiplying these factors together we get
LCM=Least number is Least number= 576-11= 576
Hence, the correct answer is option 3) 576

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