Find Least Common Multiple of 33, 77 and 60 using prime factorisation method.
Answer
LCM( 33, 77, 60 ) = 4620
Explanation
Step 1: Write down factorisation of each number:
33 = 3 · 11
77 = 7 · 11
60 = 2 · 2 · 3 · 5
Step 2 : Match primes vertically:
| 33 | = | 3 | · | 11 | ||||||||
| 77 | = | 7 | · | 11 | ||||||||
| 60 | = | 2 | · | 2 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 33 | = | 3 | · | 11 | ||||||||||
| 77 | = | 7 | · | 11 | ||||||||||
| 60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 5 | · | 7 | · | 11 | = | 4620 |
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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