Find Least Common Multiple of 110, 120 and 440 using prime factorisation method.
Answer
LCM( 110, 120, 440 ) = 1320
Explanation
Step 1: Write down factorisation of each number:
110 = 2 · 5 · 11
120 = 2 · 2 · 2 · 3 · 5
440 = 2 · 2 · 2 · 5 · 11
Step 2 : Match primes vertically:
| 110 | = | 2 | · | 5 | · | 11 | ||||||
| 120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||
| 440 | = | 2 | · | 2 | · | 2 | · | 5 | · | 11 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 110 | = | 2 | · | 5 | · | 11 | ||||||||
| 120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||||
| 440 | = | 2 | · | 2 | · | 2 | · | 5 | · | 11 | ||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 11 | = | 1320 |
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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