Mathematics
Find the least number which on decreasing by 20 is exactly divisible by 18, 21, 28 and 30.
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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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