Find Least Common Multiple of 168, 178 and 216 using prime factorisation method.
Answer
LCM( 168, 178, 216 ) = 134568
Explanation
Step 1: Write down factorisation of each number:
168 = 2 · 2 · 2 · 3 · 7
178 = 2 · 89
216 = 2 · 2 · 2 · 3 · 3 · 3
Step 2 : Match primes vertically:
| 168 | = | 2 | · | 2 | · | 2 | · | 3 | · | 7 | ||||||
| 178 | = | 2 | · | 89 | ||||||||||||
| 216 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 168 | = | 2 | · | 2 | · | 2 | · | 3 | · | 7 | ||||||||
| 178 | = | 2 | · | 89 | ||||||||||||||
| 216 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 7 | · | 89 | = | 134568 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.
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