Find Least Common Multiple of 1, 1, 7, 4, 5, 2, 3 and 28 using prime factorisation method.
Answer
LCM( 1, 1, 7, 4, 5, 2, 3, 28 ) = 420
Explanation
Step 1: Write down factorisation of each number:
1 = 1
1 = 1
7 = 7
4 = 2 · 2
5 = 5
2 = 2
3 = 3
28 = 2 · 2 · 7
Step 2 : Match primes vertically:
| 1 | = | 1 | ||||||||||
| 7 | = | 7 | ||||||||||
| 4 | = | 2 | · | 2 | ||||||||
| 5 | = | 5 | ||||||||||
| 2 | = | 2 | ||||||||||
| 3 | = | 3 | ||||||||||
| 28 | = | 2 | · | 2 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 1 | = | 1 | ||||||||||||
| 7 | = | 7 | ||||||||||||
| 4 | = | 2 | · | 2 | ||||||||||
| 5 | = | 5 | ||||||||||||
| 2 | = | 2 | ||||||||||||
| 3 | = | 3 | ||||||||||||
| 28 | = | 2 | · | 2 | · | 7 | ||||||||
| LCM | = | 1 | · | 2 | · | 2 | · | 3 | · | 5 | · | 7 | = | 420 |
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