Question
Find Least Common Multiple of 38, 46 and 84 using prime factorisation method.
Answer
LCM( 38, 46, 84 ) = 36708
Explanation
Step 1: Write down factorisation of each number:
38 = 2 · 19
46 = 2 · 23
84 = 2 · 2 · 3 · 7
Step 2 : Match primes vertically:
| 38 | = | 2 | · | 19 | ||||||||
| 46 | = | 2 | · | 23 | ||||||||
| 84 | = | 2 | · | 2 | · | 3 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 38 | = | 2 | · | 19 | ||||||||||
| 46 | = | 2 | · | 23 | ||||||||||
| 84 | = | 2 | · | 2 | · | 3 | · | 7 | ||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 7 | · | 19 | · | 23 | = | 36708 |
This solution can be visualized using a Venn diagram.
0,0
38
46
84
2
19
23
2
3
7
The LCM is equal to the product of all the numbers on the diagram.
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