Find Least Common Multiple of 42, 38 and 26 using prime factorisation method.
Answer
LCM( 42, 38, 26 ) = 10374
Explanation
Step 1: Write down factorisation of each number:
42 = 2 · 3 · 7
38 = 2 · 19
26 = 2 · 13
Step 2 : Match primes vertically:
| 42 | = | 2 | · | 3 | · | 7 | ||||
| 38 | = | 2 | · | 19 | ||||||
| 26 | = | 2 | · | 13 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 42 | = | 2 | · | 3 | · | 7 | ||||||
| 38 | = | 2 | · | 19 | ||||||||
| 26 | = | 2 | · | 13 | ||||||||
| LCM | = | 2 | · | 3 | · | 7 | · | 13 | · | 19 | = | 10374 |
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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