Find Least Common Multiple of 50, 68 and 54 using prime factorisation method.
Answer
LCM( 50, 68, 54 ) = 45900
Explanation
Step 1: Write down factorisation of each number:
50 = 2 · 5 · 5
68 = 2 · 2 · 17
54 = 2 · 3 · 3 · 3
Step 2 : Match primes vertically:
| 50 | = | 2 | · | 5 | · | 5 | ||||||||||
| 68 | = | 2 | · | 2 | · | 17 | ||||||||||
| 54 | = | 2 | · | 3 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 50 | = | 2 | · | 5 | · | 5 | ||||||||||||
| 68 | = | 2 | · | 2 | · | 17 | ||||||||||||
| 54 | = | 2 | · | 3 | · | 3 | · | 3 | ||||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 5 | · | 5 | · | 17 | = | 45900 |
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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