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Question

Which is the least number which when divided by 12, 16, 24 and 36 leaves a remainder 7 in each case?

A
121
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B
131
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C
144
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D
151
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Solution

The correct option is D 151
The least number which is divisible by 12, 16, 24 and 36 is the LCM of 12, 16, 24 and 36.
12 = 2 × 2 × 3
16 = 2 × 2 × 2× 2
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 ×3
LCM of 12, 16, 24 and 36 = 2 × 2 × 2 × 2 × 3 × 3 = 144
Therefore, least number which when divided by 12, 16, 24 and 36 leaves a remainder 7 in each case = 144 + 7 = 151.

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