Question

Find the least number which when divided by $24,36$ and $48$ leaves the remainders $21,33$ and $45$ respectively.

Answer 1

First, we need to find the LCM of 24, 36 and 48. The LCM of 24, 36 and 48 is 144.
Now, we shall find the difference of 24 and 21 which is 3. Similarly, the difference of 36 and 33 and also that of 48 and 45 is 3 respectively.
The difference between the LCM and 3 is the smallest number.
So, 144 - 3 $=$ 141.
Hence, $141$ is the smallest number when divided by 24, 36 and 48 leave remainders 21, 33 and 45 respectively.