Question
Find Least Common Multiple of 38, 57 and 95 using prime factorisation method.
Answer
LCM( 38, 57, 95 ) = 570
Explanation
Step 1: Write down factorisation of each number:
38 = 2 · 19
57 = 3 · 19
95 = 5 · 19
Step 2 : Match primes vertically:
| 38 | = | 2 | · | 19 | ||||
| 57 | = | 3 | · | 19 | ||||
| 95 | = | 5 | · | 19 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 38 | = | 2 | · | 19 | ||||||
| 57 | = | 3 | · | 19 | ||||||
| 95 | = | 5 | · | 19 | ||||||
| LCM | = | 2 | · | 3 | · | 5 | · | 19 | = | 570 |
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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