Question
Find Least Common Multiple of 4, 3, 8, 9 and 12 using prime factorisation method.
Answer
LCM( 4, 3, 8, 9, 12 ) = 72
Explanation
Step 1: Write down factorisation of each number:
4 = 2 · 2
3 = 3
8 = 2 · 2 · 2
9 = 3 · 3
12 = 2 · 2 · 3
Step 2 : Match primes vertically:
| 4 | = | 2 | · | 2 | ||||||
| 3 | = | 3 | ||||||||
| 8 | = | 2 | · | 2 | · | 2 | ||||
| 9 | = | 3 | · | 3 | ||||||
| 12 | = | 2 | · | 2 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 4 | = | 2 | · | 2 | ||||||||
| 3 | = | 3 | ||||||||||
| 8 | = | 2 | · | 2 | · | 2 | ||||||
| 9 | = | 3 | · | 3 | ||||||||
| 12 | = | 2 | · | 2 | · | 3 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | = | 72 |
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