Find Least Common Multiple of 36, 54, 108 and 144 using prime factorisation method.
Answer
LCM( 36, 54, 108, 144 ) = 432
Explanation
Step 1: Write down factorisation of each number:
36 = 2 · 2 · 3 · 3
54 = 2 · 3 · 3 · 3
108 = 2 · 2 · 3 · 3 · 3
144 = 2 · 2 · 2 · 2 · 3 · 3
Step 2 : Match primes vertically:
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||
| 54 | = | 2 | · | 3 | · | 3 | · | 3 | ||||||
| 108 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | ||||
| 144 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||||
| 54 | = | 2 | · | 3 | · | 3 | · | 3 | ||||||||
| 108 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | ||||||
| 144 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | = | 432 |
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