Question
Find Least Common Multiple of 12, 23, 7, 9, 17 and 50 using prime factorisation method.
Answer
LCM( 12, 23, 7, 9, 17, 50 ) = 2463300
Explanation
Step 1: Write down factorisation of each number:
12 = 2 · 2 · 3
23 = 23
7 = 7
9 = 3 · 3
17 = 17
50 = 2 · 5 · 5
Step 2 : Match primes vertically:
| 12 | = | 2 | · | 2 | · | 3 | ||||||||||||
| 23 | = | 23 | ||||||||||||||||
| 7 | = | 7 | ||||||||||||||||
| 9 | = | 3 | · | 3 | ||||||||||||||
| 17 | = | 17 | ||||||||||||||||
| 50 | = | 2 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 12 | = | 2 | · | 2 | · | 3 | ||||||||||||||
| 23 | = | 23 | ||||||||||||||||||
| 7 | = | 7 | ||||||||||||||||||
| 9 | = | 3 | · | 3 | ||||||||||||||||
| 17 | = | 17 | ||||||||||||||||||
| 50 | = | 2 | · | 5 | · | 5 | ||||||||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | · | 7 | · | 17 | · | 23 | = | 2463300 |
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