Question
Find Least Common Multiple of 85, 70 and 74 using prime factorisation method.
Answer
LCM( 85, 70, 74 ) = 44030
Explanation
Step 1: Write down factorisation of each number:
85 = 5 · 17
70 = 2 · 5 · 7
74 = 2 · 37
Step 2 : Match primes vertically:
| 85 | = | 5 | · | 17 | ||||||
| 70 | = | 2 | · | 5 | · | 7 | ||||
| 74 | = | 2 | · | 37 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 85 | = | 5 | · | 17 | ||||||||
| 70 | = | 2 | · | 5 | · | 7 | ||||||
| 74 | = | 2 | · | 37 | ||||||||
| LCM | = | 2 | · | 5 | · | 7 | · | 17 | · | 37 | = | 44030 |
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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