Question
Find Least Common Multiple of 2, 3, 4, 5, 6 and 7 using prime factorisation method.
Answer
LCM( 2, 3, 4, 5, 6, 7 ) = 420
Explanation
Step 1: Write down factorisation of each number:
2 = 2
3 = 3
4 = 2 · 2
5 = 5
6 = 2 · 3
7 = 7
Step 2 : Match primes vertically:
| 2 | = | 2 | ||||||||
| 3 | = | 3 | ||||||||
| 4 | = | 2 | · | 2 | ||||||
| 5 | = | 5 | ||||||||
| 6 | = | 2 | · | 3 | ||||||
| 7 | = | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 2 | = | 2 | ||||||||||
| 3 | = | 3 | ||||||||||
| 4 | = | 2 | · | 2 | ||||||||
| 5 | = | 5 | ||||||||||
| 6 | = | 2 | · | 3 | ||||||||
| 7 | = | 7 | ||||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 5 | · | 7 | = | 420 |
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