Find Least Common Multiple of 84, 175 and 198 using prime factorisation method.
Answer
LCM( 84, 175, 198 ) = 69300
Explanation
Step 1: Write down factorisation of each number:
84 = 2 · 2 · 3 · 7
175 = 5 · 5 · 7
198 = 2 · 3 · 3 · 11
Step 2 : Match primes vertically:
| 84 | = | 2 | · | 2 | · | 3 | · | 7 | ||||||||
| 175 | = | 5 | · | 5 | · | 7 | ||||||||||
| 198 | = | 2 | · | 3 | · | 3 | · | 11 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 84 | = | 2 | · | 2 | · | 3 | · | 7 | ||||||||||
| 175 | = | 5 | · | 5 | · | 7 | ||||||||||||
| 198 | = | 2 | · | 3 | · | 3 | · | 11 | ||||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | · | 7 | · | 11 | = | 69300 |
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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