Question
Find Least Common Multiple of 66, 104 and 156 using prime factorisation method.
Answer
LCM( 66, 104, 156 ) = 3432
Explanation
Step 1: Write down factorisation of each number:
66 = 2 · 3 · 11
104 = 2 · 2 · 2 · 13
156 = 2 · 2 · 3 · 13
Step 2 : Match primes vertically:
| 66 | = | 2 | · | 3 | · | 11 | ||||||
| 104 | = | 2 | · | 2 | · | 2 | · | 13 | ||||
| 156 | = | 2 | · | 2 | · | 3 | · | 13 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 66 | = | 2 | · | 3 | · | 11 | ||||||||
| 104 | = | 2 | · | 2 | · | 2 | · | 13 | ||||||
| 156 | = | 2 | · | 2 | · | 3 | · | 13 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 11 | · | 13 | = | 3432 |
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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