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Question
Find the smallest number which, on being decreased by 3, is completely divisible by 18, 36, 32 and 27.
Solution
LCM of 18, 36, 32 and 27
| 2 | 18, | 36, | 32, | 27 |
| 2 | 9, | 18, | 16, | 27 |
| 3 | 9, | 9, | 8, | 27 |
| 3 | 3, | 3, | 8, | 9 |
| 1, | 1, | 8, | 3 |
∴ L.C.M. = 2 x 2 x 3 x 3 x 3 x 8 = 864
∴ The required number = 864 + 3 = 867
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