Find Least Common Multiple of 2120, 3248 and 4872 using prime factorisation method.
Answer
LCM( 2120, 3248, 4872 ) = 2582160
Explanation
Step 1: Write down factorisation of each number:
2120 = 2 · 2 · 2 · 5 · 53
3248 = 2 · 2 · 2 · 2 · 7 · 29
4872 = 2 · 2 · 2 · 3 · 7 · 29
Step 2 : Match primes vertically:
| 2120 | = | 2 | · | 2 | · | 2 | · | 5 | · | 53 | ||||||||
| 3248 | = | 2 | · | 2 | · | 2 | · | 2 | · | 7 | · | 29 | ||||||
| 4872 | = | 2 | · | 2 | · | 2 | · | 3 | · | 7 | · | 29 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 2120 | = | 2 | · | 2 | · | 2 | · | 5 | · | 53 | ||||||||||
| 3248 | = | 2 | · | 2 | · | 2 | · | 2 | · | 7 | · | 29 | ||||||||
| 4872 | = | 2 | · | 2 | · | 2 | · | 3 | · | 7 | · | 29 | ||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 7 | · | 29 | · | 53 | = | 2582160 |
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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