Find Least Common Multiple of 6, 8, 18, 1, 2 and 9 using prime factorisation method.
Answer
LCM( 6, 8, 18, 1, 2, 9 ) = 72
Explanation
Step 1: Write down factorisation of each number:
6 = 2 · 3
8 = 2 · 2 · 2
18 = 2 · 3 · 3
1 = 1
2 = 2
9 = 3 · 3
Step 2 : Match primes vertically:
| 6 | = | 2 | · | 3 | ||||||||
| 8 | = | 2 | · | 2 | · | 2 | ||||||
| 18 | = | 2 | · | 3 | · | 3 | ||||||
| 1 | = | 1 | ||||||||||
| 2 | = | 2 | ||||||||||
| 9 | = | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 6 | = | 2 | · | 3 | ||||||||||
| 8 | = | 2 | · | 2 | · | 2 | ||||||||
| 18 | = | 2 | · | 3 | · | 3 | ||||||||
| 1 | = | 1 | ||||||||||||
| 2 | = | 2 | ||||||||||||
| 9 | = | 3 | · | 3 | ||||||||||
| LCM | = | 1 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | = | 72 |
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