Question
Find Least Common Multiple of 3, 9, 4, 16 and 10 using prime factorisation method.
Answer
LCM( 3, 9, 4, 16, 10 ) = 720
Explanation
Step 1: Write down factorisation of each number:
3 = 3
9 = 3 · 3
4 = 2 · 2
16 = 2 · 2 · 2 · 2
10 = 2 · 5
Step 2 : Match primes vertically:
| 3 | = | 3 | ||||||||||||
| 9 | = | 3 | · | 3 | ||||||||||
| 4 | = | 2 | · | 2 | ||||||||||
| 16 | = | 2 | · | 2 | · | 2 | · | 2 | ||||||
| 10 | = | 2 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 3 | = | 3 | ||||||||||||||
| 9 | = | 3 | · | 3 | ||||||||||||
| 4 | = | 2 | · | 2 | ||||||||||||
| 16 | = | 2 | · | 2 | · | 2 | · | 2 | ||||||||
| 10 | = | 2 | · | 5 | ||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | = | 720 |
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