Find the smallest number which, when divided separately by 15, 20, 36, and 48, leaves a remainder of 3 in each case.

Step 1: Form equation

Let the number be $N$

Then:
$N - 3$ is divisible by 15, 20, 36, 48

So,
$N - 3 = \text{LCM of } (15, 20, 36, 48)$

Step 2: Find LCM

• $15 = 3 \times 5$
• $20 = 2^2 \times 5$
• $36 = 2^2 \times 3^2$
• $48 = 2^4 \times 3$

LCM = $2^4 \times 3^2 \times 5 = 16 \times 9 \times 5 = 720$

Step 3: Find number

$N = 720 + 3 = 723$

Final Answer: 723