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What least number when divided by 36, 24 and 16 leaves 11 as remainder in each case?
- a)36
- b)133
- c)144
- d)155
- e)166
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
What least number when divided by 36, 24 and 16 leaves 11 as remainder...
Here least number is needed that means we need the LCM
We must first find LCM of 36, 24 and 16
We must first find LCM of 36, 24 and 16
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What least number when divided by 36, 24 and 16 leaves 11 as remainder...
Solution:
To find the least number that leaves the same remainder when divided by 36, 24 and 16, we need to find the LCM of 36, 24 and 16.
Prime factorization of 36 = 2^2 × 3^2
Prime factorization of 24 = 2^3 × 3^1
Prime factorization of 16 = 2^4
LCM of 36, 24, and 16 is 2^4 × 3^2 = 144
Therefore, any number that leaves the remainder of 11 when divided by 36, 24, and 16 is a multiple of 144 plus 11.
The least multiple of 144 greater than 11 is 144 itself. So, the least number that leaves the remainder of 11 when divided by 36, 24, and 16 is 144 + 11 = 155.
Hence, the correct answer is option D) 155.
To find the least number that leaves the same remainder when divided by 36, 24 and 16, we need to find the LCM of 36, 24 and 16.
Prime factorization of 36 = 2^2 × 3^2
Prime factorization of 24 = 2^3 × 3^1
Prime factorization of 16 = 2^4
LCM of 36, 24, and 16 is 2^4 × 3^2 = 144
Therefore, any number that leaves the remainder of 11 when divided by 36, 24, and 16 is a multiple of 144 plus 11.
The least multiple of 144 greater than 11 is 144 itself. So, the least number that leaves the remainder of 11 when divided by 36, 24, and 16 is 144 + 11 = 155.
Hence, the correct answer is option D) 155.
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What least number when divided by 36, 24 and 16 leaves 11 as remainder...
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What least number when divided by 36, 24 and 16 leaves 11 as remainder in each case?a)36b)133c)144d)155e)166Correct answer is option 'D'. Can you explain this answer?
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