Question
Find Least Common Multiple of 17, 23 and 29 using prime factorisation method.
Answer
LCM( 17, 23, 29 ) = 11339
Explanation
Step 1: Write down factorisation of each number:
17 = 17
23 = 23
29 = 29
Step 2 : Match primes vertically:
| 17 | = | 17 | ||||
| 23 | = | 23 | ||||
| 29 | = | 29 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 17 | = | 17 | ||||||
| 23 | = | 23 | ||||||
| 29 | = | 29 | ||||||
| LCM | = | 17 | · | 23 | · | 29 | = | 11339 |
This solution can be visualized using a Venn diagram.
0,0
17
23
29
17
23
29
The LCM is equal to the product of all the numbers on the diagram.
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