Find Least Common Multiple of 12, 18, 72 and 84 using prime factorisation method.
Answer
LCM( 12, 18, 72, 84 ) = 504
Explanation
Step 1: Write down factorisation of each number:
12 = 2 · 2 · 3
18 = 2 · 3 · 3
72 = 2 · 2 · 2 · 3 · 3
84 = 2 · 2 · 3 · 7
Step 2 : Match primes vertically:
| 12 | = | 2 | · | 2 | · | 3 | ||||||
| 18 | = | 2 | · | 3 | · | 3 | ||||||
| 72 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||
| 84 | = | 2 | · | 2 | · | 3 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 12 | = | 2 | · | 2 | · | 3 | ||||||||
| 18 | = | 2 | · | 3 | · | 3 | ||||||||
| 72 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||
| 84 | = | 2 | · | 2 | · | 3 | · | 7 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 7 | = | 504 |
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