Find the least number which when divided by 24,32and 36 leaves the remainder 19,27,31 respectively
Answers
Step-by-step explanation:
24-19=5
32-27=5
36-31=5
Required number LCM=(24 32 36)=288
288-5=283 ANS........
Least number which when divided by 24, 32a nd 36 leaves the remainder 19, 27, 31 respectively is 283
Solution:
Given that,
We have to find the least number which when divided by 24, 32 and 36 leaves the remainder 19, 27, 31 respectively
Numbers = 24, 32 , 36
Reaminders = 19, 27, 31
24 - 19 = 5
32 - 27 = 5
36 - 31 = 5
Difference = 5
Thus the least number is: LCM of 24, 32 , 36 - 5
Find LCM of 24, 32 , 36:
List all prime factors for each number
Prime Factorization of 24 is: 2 x 2 x 2 x 3
Prime Factorization of 32 is: 2 x 2 x 2 x 2 x 2
Prime Factorization of 36 is: 2 x 2 x 3 x 3
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, 3, 3
Multiply these factors together to find the LCM
LCM = 2 x 2 x 2 x 2 x 2 x 3 x 3 = 288
Therefore,
Least number = 288 - 5 = 283
Thus least number which when divided by 24, 32a nd 36 leaves the remainder 19, 27, 31 respectively is 283
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