Find Least Common Multiple of 60, 80 and 124 using prime factorisation method.
Answer
LCM( 60, 80, 124 ) = 7440
Explanation
Step 1: Write down factorisation of each number:
60 = 2 · 2 · 3 · 5
80 = 2 · 2 · 2 · 2 · 5
124 = 2 · 2 · 31
Step 2 : Match primes vertically:
| 60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||||
| 80 | = | 2 | · | 2 | · | 2 | · | 2 | · | 5 | ||||
| 124 | = | 2 | · | 2 | · | 31 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||||||
| 80 | = | 2 | · | 2 | · | 2 | · | 2 | · | 5 | ||||||
| 124 | = | 2 | · | 2 | · | 31 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 31 | = | 7440 |
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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