Question
Find Least Common Multiple of 96, 68 and 5 using prime factorisation method.
Answer
LCM( 96, 68, 5 ) = 8160
Explanation
Step 1: Write down factorisation of each number:
96 = 2 · 2 · 2 · 2 · 2 · 3
68 = 2 · 2 · 17
5 = 5
Step 2 : Match primes vertically:
| 96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||
| 68 | = | 2 | · | 2 | · | 17 | ||||||||||
| 5 | = | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||
| 68 | = | 2 | · | 2 | · | 17 | ||||||||||||
| 5 | = | 5 | ||||||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 17 | = | 8160 |
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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