Question
Find Least Common Multiple of 1, 3, 5, 6, 2, 9, 4 and 27 using prime factorisation method.
Answer
LCM( 1, 3, 5, 6, 2, 9, 4, 27 ) = 540
Explanation
Step 1: Write down factorisation of each number:
1 = 1
3 = 3
5 = 5
6 = 2 · 3
2 = 2
9 = 3 · 3
4 = 2 · 2
27 = 3 · 3 · 3
Step 2 : Match primes vertically:
| 1 | = | 1 | ||||||||||||
| 3 | = | 3 | ||||||||||||
| 5 | = | 5 | ||||||||||||
| 6 | = | 2 | · | 3 | ||||||||||
| 2 | = | 2 | ||||||||||||
| 9 | = | 3 | · | 3 | ||||||||||
| 4 | = | 2 | · | 2 | ||||||||||
| 27 | = | 3 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 1 | = | 1 | ||||||||||||||
| 3 | = | 3 | ||||||||||||||
| 5 | = | 5 | ||||||||||||||
| 6 | = | 2 | · | 3 | ||||||||||||
| 2 | = | 2 | ||||||||||||||
| 9 | = | 3 | · | 3 | ||||||||||||
| 4 | = | 2 | · | 2 | ||||||||||||
| 27 | = | 3 | · | 3 | · | 3 | ||||||||||
| LCM | = | 1 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 5 | = | 540 |
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