Mathematics
Find the least number which when divided by 24, 36, 45 and 54 leaves a remainder of 3 in each case.
Answer
First, we find the LCM of 24, 36, 45 and 54.
| 2 | 24, 36, 45, 54 |
|---|---|
| 2 | 12, 18, 45, 27 |
| 2 | 6, 9, 45, 27 |
| 3 | 3, 9, 45, 27 |
| 3 | 1, 3, 15, 9 |
| 3 | 1, 1, 5, 3 |
| 5 | 1, 1, 5, 1 |
| 1, 1, 1, 1 |
LCM of 24, 36, 45 and 54 = 2 × 2 × 2 × 3 × 3 × 3 × 5 = 1080.
The required least number which leaves remainder 3 = 1080 + 3 = 1083.
Hence, the required least number is 1083.
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