Find Least Common Multiple of 415, 860 and 690 using prime factorisation method.
Answer
LCM( 415, 860, 690 ) = 4925220
Explanation
Step 1: Write down factorisation of each number:
415 = 5 · 83
860 = 2 · 2 · 5 · 43
690 = 2 · 3 · 5 · 23
Step 2 : Match primes vertically:
| 415 | = | 5 | · | 83 | ||||||||||
| 860 | = | 2 | · | 2 | · | 5 | · | 43 | ||||||
| 690 | = | 2 | · | 3 | · | 5 | · | 23 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 415 | = | 5 | · | 83 | ||||||||||||
| 860 | = | 2 | · | 2 | · | 5 | · | 43 | ||||||||
| 690 | = | 2 | · | 3 | · | 5 | · | 23 | ||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 5 | · | 23 | · | 43 | · | 83 | = | 4925220 |
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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