Find Least Common Multiple of 42, 58 and 85 using prime factorisation method.
Answer
LCM( 42, 58, 85 ) = 103530
Explanation
Step 1: Write down factorisation of each number:
42 = 2 · 3 · 7
58 = 2 · 29
85 = 5 · 17
Step 2 : Match primes vertically:
| 42 | = | 2 | · | 3 | · | 7 | ||||||
| 58 | = | 2 | · | 29 | ||||||||
| 85 | = | 5 | · | 17 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 42 | = | 2 | · | 3 | · | 7 | ||||||||
| 58 | = | 2 | · | 29 | ||||||||||
| 85 | = | 5 | · | 17 | ||||||||||
| LCM | = | 2 | · | 3 | · | 5 | · | 7 | · | 17 | · | 29 | = | 103530 |
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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