Find Least Common Multiple of 80, 96 and 105 using prime factorisation method.
Answer
LCM( 80, 96, 105 ) = 3360
Explanation
Step 1: Write down factorisation of each number:
80 = 2 · 2 · 2 · 2 · 5
96 = 2 · 2 · 2 · 2 · 2 · 3
105 = 3 · 5 · 7
Step 2 : Match primes vertically:
| 80 | = | 2 | · | 2 | · | 2 | · | 2 | · | 5 | ||||||
| 96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||
| 105 | = | 3 | · | 5 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 80 | = | 2 | · | 2 | · | 2 | · | 2 | · | 5 | ||||||||
| 96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||
| 105 | = | 3 | · | 5 | · | 7 | ||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 7 | = | 3360 |
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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