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Question
Which two consecutive even numbers have an LCM of 180?
Solution
Two consecutive even numbers' LCM = 180
The HCF of two consecutive even numbers, on the other hand, = 2
Now, the given number's Product = HCF × LCM
= 2 × 180
= 360
We must factor 360 to find two consecutive even numbers.
| 2 | 360 |
| 2 | 180 |
| 2 | 90 |
| 3 | 45 |
| 3 | 15 |
| 5 | 5 |
| 1 |
360 = (2 × 2 × 2) × (3 × 3 × 5)
= (2 × 3 × 3) × (2 × 2 × 5)
= 18 × 20
∴ 18 and 20 are two consecutive even numbers whose LCM is 180.
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