Question
Find Least Common Multiple of 966, 346 and 926 using prime factorisation method.
Answer
LCM( 966, 346, 926 ) = 77375634
Explanation
Step 1: Write down factorisation of each number:
966 = 2 · 3 · 7 · 23
346 = 2 · 173
926 = 2 · 463
Step 2 : Match primes vertically:
| 966 | = | 2 | · | 3 | · | 7 | · | 23 | ||||
| 346 | = | 2 | · | 173 | ||||||||
| 926 | = | 2 | · | 463 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 966 | = | 2 | · | 3 | · | 7 | · | 23 | ||||||
| 346 | = | 2 | · | 173 | ||||||||||
| 926 | = | 2 | · | 463 | ||||||||||
| LCM | = | 2 | · | 3 | · | 7 | · | 23 | · | 173 | · | 463 | = | 77375634 |
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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