Question
Find Least Common Multiple of 18, 24, 30 and 12 using prime factorisation method.
Answer
LCM( 18, 24, 30, 12 ) = 360
Explanation
Step 1: Write down factorisation of each number:
18 = 2 · 3 · 3
24 = 2 · 2 · 2 · 3
30 = 2 · 3 · 5
12 = 2 · 2 · 3
Step 2 : Match primes vertically:
| 18 | = | 2 | · | 3 | · | 3 | ||||||
| 24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||
| 30 | = | 2 | · | 3 | · | 5 | ||||||
| 12 | = | 2 | · | 2 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 18 | = | 2 | · | 3 | · | 3 | ||||||||
| 24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||||
| 30 | = | 2 | · | 3 | · | 5 | ||||||||
| 12 | = | 2 | · | 2 | · | 3 | ||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | = | 360 |
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