Find Least Common Multiple of 728, 166 and 198 using prime factorisation method.
Answer
LCM( 728, 166, 198 ) = 5981976
Explanation
Step 1: Write down factorisation of each number:
728 = 2 · 2 · 2 · 7 · 13
166 = 2 · 83
198 = 2 · 3 · 3 · 11
Step 2 : Match primes vertically:
| 728 | = | 2 | · | 2 | · | 2 | · | 7 | · | 13 | ||||||||
| 166 | = | 2 | · | 83 | ||||||||||||||
| 198 | = | 2 | · | 3 | · | 3 | · | 11 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 728 | = | 2 | · | 2 | · | 2 | · | 7 | · | 13 | ||||||||||
| 166 | = | 2 | · | 83 | ||||||||||||||||
| 198 | = | 2 | · | 3 | · | 3 | · | 11 | ||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 7 | · | 11 | · | 13 | · | 83 | = | 5981976 |
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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