Find Least Common Multiple of 22, 54, 108, 135 and 198 using prime factorisation method.
Answer
LCM( 22, 54, 108, 135, 198 ) = 5940
Explanation
Step 1: Write down factorisation of each number:
22 = 2 · 11
54 = 2 · 3 · 3 · 3
108 = 2 · 2 · 3 · 3 · 3
135 = 3 · 3 · 3 · 5
198 = 2 · 3 · 3 · 11
Step 2 : Match primes vertically:
| 22 | = | 2 | · | 11 | ||||||||||
| 54 | = | 2 | · | 3 | · | 3 | · | 3 | ||||||
| 108 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | ||||
| 135 | = | 3 | · | 3 | · | 3 | · | 5 | ||||||
| 198 | = | 2 | · | 3 | · | 3 | · | 11 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 22 | = | 2 | · | 11 | ||||||||||||
| 54 | = | 2 | · | 3 | · | 3 | · | 3 | ||||||||
| 108 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | ||||||
| 135 | = | 3 | · | 3 | · | 3 | · | 5 | ||||||||
| 198 | = | 2 | · | 3 | · | 3 | · | 11 | ||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 5 | · | 11 | = | 5940 |
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