Question
Find Least Common Multiple of 12, 16, 17 and 36 using prime factorisation method.
Answer
LCM( 12, 16, 17, 36 ) = 2448
Explanation
Step 1: Write down factorisation of each number:
12 = 2 · 2 · 3
16 = 2 · 2 · 2 · 2
17 = 17
36 = 2 · 2 · 3 · 3
Step 2 : Match primes vertically:
| 12 | = | 2 | · | 2 | · | 3 | ||||||||
| 16 | = | 2 | · | 2 | · | 2 | · | 2 | ||||||
| 17 | = | 17 | ||||||||||||
| 36 | = | 2 | · | 2 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 12 | = | 2 | · | 2 | · | 3 | ||||||||||
| 16 | = | 2 | · | 2 | · | 2 | · | 2 | ||||||||
| 17 | = | 17 | ||||||||||||||
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 17 | = | 2448 |
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