Question
Find Least Common Multiple of 57 and 85 using prime factorisation method.
Answer
LCM( 57, 85 ) = 4845
Explanation
Step 1: Write down factorisation of each number:
57 = 3 · 19
85 = 5 · 17
Step 2 : Match primes vertically:
| 57 | = | 3 | · | 19 | ||||
| 85 | = | 5 | · | 17 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 57 | = | 3 | · | 19 | ||||||
| 85 | = | 5 | · | 17 | ||||||
| LCM | = | 3 | · | 5 | · | 17 | · | 19 | = | 4845 |
This solution can be visualized using a Venn diagram.
0,0
57
85
3
19
5
17
The LCM is equal to the product of all the numbers on the diagram.
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