Question
Find Least Common Multiple of 39, 52 and 65 using prime factorisation method.
Answer
LCM( 39, 52, 65 ) = 780
Explanation
Step 1: Write down factorisation of each number:
39 = 3 · 13
52 = 2 · 2 · 13
65 = 5 · 13
Step 2 : Match primes vertically:
| 39 | = | 3 | · | 13 | ||||||
| 52 | = | 2 | · | 2 | · | 13 | ||||
| 65 | = | 5 | · | 13 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 39 | = | 3 | · | 13 | ||||||||
| 52 | = | 2 | · | 2 | · | 13 | ||||||
| 65 | = | 5 | · | 13 | ||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 5 | · | 13 | = | 780 |
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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