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Question
Find the LCM of the following numbers:
- 9 and 4
- 12 and 5
- 6 and 5
- 15 and 4
Observe a common property in the obtained LCMs. Is LCM the product of two numbers in each case?
Solution
(a)
| 2 | 9, 4 |
| 2 | 9, 2 |
| 3 | 9, 1 |
| 3 | 3, 1 |
| 1, 1 |
LCM = 2 × 2 × 3 × 3 = 36
(b)
| 2 | 12, 5 |
| 2 | 6, 5 |
| 3 | 3, 5 |
| 5 | 1, 5 |
| 1, 1 |
LCM = 2 × 2 × 3 × 5 = 60
(c)
| 2 | 6, 5 |
| 3 | 3, 5 |
| 5 | 1, 5 |
| 1, 1 |
LCM = 2 × 3 × 5 = 30
(d)
| 2 | 15, 4 |
| 2 | 15, 2 |
| 3 | 15, 1 |
| 5 | 5, 1 |
| 1, 1 |
LCM = 2 × 2 × 3 × 5 = 60
Yes, it can be observed that in each case, the LCM of the given numbers is the product of these numbers. When two numbers are co-prime, their LCM is the product of those numbers. Also, in each case, LCM is a multiple of 3.
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