Question
Find Least Common Multiple of 110, 121 and 132 using prime factorisation method.
Answer
LCM( 110, 121, 132 ) = 7260
Explanation
Step 1: Write down factorisation of each number:
110 = 2 · 5 · 11
121 = 11 · 11
132 = 2 · 2 · 3 · 11
Step 2 : Match primes vertically:
| 110 | = | 2 | · | 5 | · | 11 | ||||||
| 121 | = | 11 | · | 11 | ||||||||
| 132 | = | 2 | · | 2 | · | 3 | · | 11 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 110 | = | 2 | · | 5 | · | 11 | ||||||||
| 121 | = | 11 | · | 11 | ||||||||||
| 132 | = | 2 | · | 2 | · | 3 | · | 11 | ||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 5 | · | 11 | · | 11 | = | 7260 |
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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