Question
Find Least Common Multiple of 12, 16, 18, 21 and 28 using prime factorisation method.
Answer
LCM( 12, 16, 18, 21, 28 ) = 1008
Explanation
Step 1: Write down factorisation of each number:
12 = 2 · 2 · 3
16 = 2 · 2 · 2 · 2
18 = 2 · 3 · 3
21 = 3 · 7
28 = 2 · 2 · 7
Step 2 : Match primes vertically:
| 12 | = | 2 | · | 2 | · | 3 | ||||||||
| 16 | = | 2 | · | 2 | · | 2 | · | 2 | ||||||
| 18 | = | 2 | · | 3 | · | 3 | ||||||||
| 21 | = | 3 | · | 7 | ||||||||||
| 28 | = | 2 | · | 2 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 12 | = | 2 | · | 2 | · | 3 | ||||||||||
| 16 | = | 2 | · | 2 | · | 2 | · | 2 | ||||||||
| 18 | = | 2 | · | 3 | · | 3 | ||||||||||
| 21 | = | 3 | · | 7 | ||||||||||||
| 28 | = | 2 | · | 2 | · | 7 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 7 | = | 1008 |
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