Find Least Common Multiple of 117, 143 and 104 using prime factorisation method.
Answer
LCM( 117, 143, 104 ) = 10296
Explanation
Step 1: Write down factorisation of each number:
117 = 3 · 3 · 13
143 = 11 · 13
104 = 2 · 2 · 2 · 13
Step 2 : Match primes vertically:
| 117 | = | 3 | · | 3 | · | 13 | ||||||||
| 143 | = | 11 | · | 13 | ||||||||||
| 104 | = | 2 | · | 2 | · | 2 | · | 13 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 117 | = | 3 | · | 3 | · | 13 | ||||||||||
| 143 | = | 11 | · | 13 | ||||||||||||
| 104 | = | 2 | · | 2 | · | 2 | · | 13 | ||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 11 | · | 13 | = | 10296 |
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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