Find Least Common Multiple of 1, 2, 3, 10, 20 and 60 using prime factorisation method.
Answer
LCM( 1, 2, 3, 10, 20, 60 ) = 60
Explanation
Step 1: Write down factorisation of each number:
1 = 1
2 = 2
3 = 3
10 = 2 · 5
20 = 2 · 2 · 5
60 = 2 · 2 · 3 · 5
Step 2 : Match primes vertically:
| 1 | = | 1 | ||||||||
| 2 | = | 2 | ||||||||
| 3 | = | 3 | ||||||||
| 10 | = | 2 | · | 5 | ||||||
| 20 | = | 2 | · | 2 | · | 5 | ||||
| 60 | = | 2 | · | 2 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 1 | = | 1 | ||||||||||
| 2 | = | 2 | ||||||||||
| 3 | = | 3 | ||||||||||
| 10 | = | 2 | · | 5 | ||||||||
| 20 | = | 2 | · | 2 | · | 5 | ||||||
| 60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||
| LCM | = | 1 | · | 2 | · | 2 | · | 3 | · | 5 | = | 60 |
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