Mathematics
Find the least number which on decreasing by 20 is exactly divisible by 18, 21, 28 and 30.
Answer
First, we find the LCM of 18, 21, 28 and 30.
| 2 | 18, 21, 28, 30 |
|---|---|
| 2 | 9, 21, 14, 15 |
| 3 | 9, 21, 7, 15 |
| 3 | 3, 7, 7, 5 |
| 5 | 1, 7, 7, 5 |
| 7 | 1, 7, 7, 1 |
| 1, 1, 1, 1 |
LCM of 18, 21, 28 and 30 = 2 × 2 × 3 × 3 × 5 × 7 = 1260.
According to given condition, the required number, when decreased by 20, gives 1260.
The required number = 1260 + 20 = 1280.
Hence, the required least number is 1280.
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