Question
Find Least Common Multiple of 12, 14, 16, 35 and 84 using prime factorisation method.
Answer
LCM( 12, 14, 16, 35, 84 ) = 1680
Explanation
Step 1: Write down factorisation of each number:
12 = 2 · 2 · 3
14 = 2 · 7
16 = 2 · 2 · 2 · 2
35 = 5 · 7
84 = 2 · 2 · 3 · 7
Step 2 : Match primes vertically:
| 12 | = | 2 | · | 2 | · | 3 | ||||||||
| 14 | = | 2 | · | 7 | ||||||||||
| 16 | = | 2 | · | 2 | · | 2 | · | 2 | ||||||
| 35 | = | 5 | · | 7 | ||||||||||
| 84 | = | 2 | · | 2 | · | 3 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 12 | = | 2 | · | 2 | · | 3 | ||||||||||
| 14 | = | 2 | · | 7 | ||||||||||||
| 16 | = | 2 | · | 2 | · | 2 | · | 2 | ||||||||
| 35 | = | 5 | · | 7 | ||||||||||||
| 84 | = | 2 | · | 2 | · | 3 | · | 7 | ||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 7 | = | 1680 |
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