Find Least Common Multiple of 6, 6, 7, 5, 20, 2 and 8 using prime factorisation method.
Answer
LCM( 6, 6, 7, 5, 20, 2, 8 ) = 840
Explanation
Step 1: Write down factorisation of each number:
6 = 2 · 3
6 = 2 · 3
7 = 7
5 = 5
20 = 2 · 2 · 5
2 = 2
8 = 2 · 2 · 2
Step 2 : Match primes vertically:
| 6 | = | 2 | · | 3 | ||||||||
| 7 | = | 7 | ||||||||||
| 5 | = | 5 | ||||||||||
| 20 | = | 2 | · | 2 | · | 5 | ||||||
| 2 | = | 2 | ||||||||||
| 8 | = | 2 | · | 2 | · | 2 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 6 | = | 2 | · | 3 | ||||||||||
| 7 | = | 7 | ||||||||||||
| 5 | = | 5 | ||||||||||||
| 20 | = | 2 | · | 2 | · | 5 | ||||||||
| 2 | = | 2 | ||||||||||||
| 8 | = | 2 | · | 2 | · | 2 | ||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 7 | = | 840 |
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