Question
Find Least Common Multiple of 6, 9, 12, 15 and 18 using prime factorisation method.
Answer
LCM( 6, 9, 12, 15, 18 ) = 180
Explanation
Step 1: Write down factorisation of each number:
6 = 2 · 3
9 = 3 · 3
12 = 2 · 2 · 3
15 = 3 · 5
18 = 2 · 3 · 3
Step 2 : Match primes vertically:
| 6 | = | 2 | · | 3 | ||||||
| 9 | = | 3 | · | 3 | ||||||
| 12 | = | 2 | · | 2 | · | 3 | ||||
| 15 | = | 3 | · | 5 | ||||||
| 18 | = | 2 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 6 | = | 2 | · | 3 | ||||||||
| 9 | = | 3 | · | 3 | ||||||||
| 12 | = | 2 | · | 2 | · | 3 | ||||||
| 15 | = | 3 | · | 5 | ||||||||
| 18 | = | 2 | · | 3 | · | 3 | ||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 3 | · | 5 | = | 180 |
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