Question

# Find the least number which when divided by 12, 15, 18 and 24 leaves a remainder 5 in each case.

A
360
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B
300
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C
365
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D
355
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Solution

## The correct option is C 365The least number that is exactly divisible by 12, 15,18 and 24 is the LCM of the three numbers. 212,15,18,2426,15,9,1223,15,9,633,15,9,331,5,3,151,5,1,11,1,1,1 L.C.M. of 12, 16, 24, 36 =2×2×2×3×3×5=360 360 is the least number which when divided by the given numbers will leave remainder 0 in each case. Therefore, the least number which when divided by 12, 15, 18 and 24 leaves a remainder 5 in each case = 360 + 5 = 365

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