Question
Find Least Common Multiple of 49, 121 and 35 using prime factorisation method.
Answer
LCM( 49, 121, 35 ) = 29645
Explanation
Step 1: Write down factorisation of each number:
49 = 7 · 7
121 = 11 · 11
35 = 5 · 7
Step 2 : Match primes vertically:
| 49 | = | 7 | · | 7 | ||||||
| 121 | = | 11 | · | 11 | ||||||
| 35 | = | 5 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 49 | = | 7 | · | 7 | ||||||||
| 121 | = | 11 | · | 11 | ||||||||
| 35 | = | 5 | · | 7 | ||||||||
| LCM | = | 5 | · | 7 | · | 7 | · | 11 | · | 11 | = | 29645 |
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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