Find Least Common Multiple of 26, 96 and 102 using prime factorisation method.
Answer
LCM( 26, 96, 102 ) = 21216
Explanation
Step 1: Write down factorisation of each number:
26 = 2 · 13
96 = 2 · 2 · 2 · 2 · 2 · 3
102 = 2 · 3 · 17
Step 2 : Match primes vertically:
| 26 | = | 2 | · | 13 | ||||||||||||
| 96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||
| 102 | = | 2 | · | 3 | · | 17 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 26 | = | 2 | · | 13 | ||||||||||||||
| 96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||
| 102 | = | 2 | · | 3 | · | 17 | ||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 13 | · | 17 | = | 21216 |
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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