Question
Find Least Common Multiple of 504 and 314 using prime factorisation method.
Answer
LCM( 504, 314 ) = 79128
Explanation
Step 1: Write down factorisation of each number:
504 = 2 · 2 · 2 · 3 · 3 · 7
314 = 2 · 157
Step 2 : Match primes vertically:
| 504 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 7 | ||
| 314 | = | 2 | · | 157 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 504 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 7 | ||||
| 314 | = | 2 | · | 157 | ||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 7 | · | 157 | = | 79128 |
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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