Discussion
The least number, which when divided by 12, 16, 24 and 36 leaves a remainder of 3, is
Answer: A
The number is 147.
A number that leaves remainder 3 on division by each of 12, 16, 24 and 36 is 3 more than a common multiple of them. The least common multiple is
\[ \begin{aligned} 12 &= 2^{2}\cdot 3,\ 16 = 2^{4},\ 24 = 2^{3}\cdot 3,\ 36 = 2^{2}\cdot 3^{2} \\ \text{LCM} &= 2^{4}\cdot 3^{2} = 144 \end{aligned} \]
so the least such number is 144 + 3 = 147. 144 itself leaves remainder 0, 141 is 3 less than the LCM, and 145 leaves remainder 1.
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