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Question
Find the smallest number which, when increased by one is exactly divisible by 12, 18, 24, 32 and 40
Solution
L.C.M. of given numbers
| 2 | 12, | 18, | 24, | 32, | 40 |
| 2 | 6, | 9, | 12, | 16, | 20 |
| 2 | 3, | 9, | 6, | 8, | 10 |
| 3 | 3, | 9, | 3, | 4, | 5 |
| 1, | 3, | 1, | 4, | 5 |
∴ L.C.M. = 2 x 2 x 2 x 3 x 3 x 4 x 5 = 1440 = One increasing
∴ The required number = 1440 - 1 = 1439
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