Find Least Common Multiple of 6976 and 7695 using prime factorisation method.
Answer
LCM( 6976, 7695 ) = 53680320
Explanation
Step 1: Write down factorisation of each number:
6976 = 2 · 2 · 2 · 2 · 2 · 2 · 109
7695 = 3 · 3 · 3 · 3 · 5 · 19
Step 2 : Match primes vertically:
| 6976 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 109 | ||||||||||||
| 7695 | = | 3 | · | 3 | · | 3 | · | 3 | · | 5 | · | 19 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 6976 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 109 | ||||||||||||||
| 7695 | = | 3 | · | 3 | · | 3 | · | 3 | · | 5 | · | 19 | ||||||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 3 | · | 5 | · | 19 | · | 109 | = | 53680320 |
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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