Question
Find Least Common Multiple of 9, 18, 6, 36 and 12 using prime factorisation method.
Answer
LCM( 9, 18, 6, 36, 12 ) = 36
Explanation
Step 1: Write down factorisation of each number:
9 = 3 · 3
18 = 2 · 3 · 3
6 = 2 · 3
36 = 2 · 2 · 3 · 3
12 = 2 · 2 · 3
Step 2 : Match primes vertically:
| 9 | = | 3 | · | 3 | ||||
| 18 | = | 2 | · | 3 | · | 3 | ||
| 6 | = | 2 | · | 3 | ||||
| 36 | = | 2 | · | 2 | · | 3 | · | 3 |
| 12 | = | 2 | · | 2 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 9 | = | 3 | · | 3 | ||||||
| 18 | = | 2 | · | 3 | · | 3 | ||||
| 6 | = | 2 | · | 3 | ||||||
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||
| 12 | = | 2 | · | 2 | · | 3 | ||||
| LCM | = | 2 | · | 2 | · | 3 | · | 3 | = | 36 |
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