Question
Find Least Common Multiple of 10, 8, 6, 8, 3, 5 and 7 using prime factorisation method.
Answer
LCM( 10, 8, 6, 8, 3, 5, 7 ) = 840
Explanation
Step 1: Write down factorisation of each number:
10 = 2 · 5
8 = 2 · 2 · 2
6 = 2 · 3
8 = 2 · 2 · 2
3 = 3
5 = 5
7 = 7
Step 2 : Match primes vertically:
| 10 | = | 2 | · | 5 | ||||||||
| 8 | = | 2 | · | 2 | · | 2 | ||||||
| 6 | = | 2 | · | 3 | ||||||||
| 3 | = | 3 | ||||||||||
| 5 | = | 5 | ||||||||||
| 7 | = | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 10 | = | 2 | · | 5 | ||||||||||
| 8 | = | 2 | · | 2 | · | 2 | ||||||||
| 6 | = | 2 | · | 3 | ||||||||||
| 3 | = | 3 | ||||||||||||
| 5 | = | 5 | ||||||||||||
| 7 | = | 7 | ||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 7 | = | 840 |
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