Question
Find Least Common Multiple of 16, 3, 4, 6, 2, 6 and 7 using prime factorisation method.
Answer
LCM( 16, 3, 4, 6, 2, 6, 7 ) = 336
Explanation
Step 1: Write down factorisation of each number:
16 = 2 · 2 · 2 · 2
3 = 3
4 = 2 · 2
6 = 2 · 3
2 = 2
6 = 2 · 3
7 = 7
Step 2 : Match primes vertically:
| 16 | = | 2 | · | 2 | · | 2 | · | 2 | ||||
| 3 | = | 3 | ||||||||||
| 4 | = | 2 | · | 2 | ||||||||
| 6 | = | 2 | · | 3 | ||||||||
| 2 | = | 2 | ||||||||||
| 7 | = | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 16 | = | 2 | · | 2 | · | 2 | · | 2 | ||||||
| 3 | = | 3 | ||||||||||||
| 4 | = | 2 | · | 2 | ||||||||||
| 6 | = | 2 | · | 3 | ||||||||||
| 2 | = | 2 | ||||||||||||
| 7 | = | 7 | ||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 7 | = | 336 |
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