Find Least Common Multiple of 56, 67 and 85 using prime factorisation method.
Answer
LCM( 56, 67, 85 ) = 318920
Explanation
Step 1: Write down factorisation of each number:
56 = 2 · 2 · 2 · 7
67 = 67
85 = 5 · 17
Step 2 : Match primes vertically:
| 56 | = | 2 | · | 2 | · | 2 | · | 7 | ||||||
| 67 | = | 67 | ||||||||||||
| 85 | = | 5 | · | 17 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 56 | = | 2 | · | 2 | · | 2 | · | 7 | ||||||||
| 67 | = | 67 | ||||||||||||||
| 85 | = | 5 | · | 17 | ||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 5 | · | 7 | · | 17 | · | 67 | = | 318920 |
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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