Find the least number which when divided by 36 48 and 64 leaves remainder 25 37 and 53 respectively
Answers
The least number which when divided by 36 48 and 64 leaves remainder 25 37 and 53 respectively is 565
Solution:
Given that,
We have to find the least number which when divided by 36 48 and 64 leaves remainder 25 37 and 53 respectively
36 - 25 = 11
48 - 37 = 11
64 - 53 = 11
Thus,
Least number = (LCM of 36, 48 , 64 ) - 11
Find the LCM of 36, 48 , 64
List all prime factors for each number.
Prime Factorization of 36 is: 2 x 2 x 3 x 3
Prime Factorization of 48 is: 2 x 2 x 2 x 2 x 3
Prime Factorization of 64 is: 2 x 2 x 2 x 2 x 2 x 2
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
2, 2, 2, 2, 2, 2, 3, 3
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 = 576
Thus,
Least number = (LCM of 36, 48 , 64 ) - 11
Least number = 576 - 11
Least number = 565
Thus the least number which when divided by 36 48 and 64 leaves remainder 25 37 and 53 respectively is 565
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