Question
Find Least Common Multiple of 40, 37 and 5 using prime factorisation method.
Answer
LCM( 40, 37, 5 ) = 1480
Explanation
Step 1: Write down factorisation of each number:
40 = 2 · 2 · 2 · 5
37 = 37
5 = 5
Step 2 : Match primes vertically:
| 40 | = | 2 | · | 2 | · | 2 | · | 5 | ||
| 37 | = | 37 | ||||||||
| 5 | = | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 40 | = | 2 | · | 2 | · | 2 | · | 5 | ||||
| 37 | = | 37 | ||||||||||
| 5 | = | 5 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 5 | · | 37 | = | 1480 |
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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