Find Least Common Multiple of 7, 8 and 14 using prime factorisation method.
Answer
LCM( 7, 8, 14 ) = 56
Explanation
Step 1: Write down factorisation of each number:
7 = 7
8 = 2 · 2 · 2
14 = 2 · 7
Step 2 : Match primes vertically:
| 7 | = | 7 | ||||||
| 8 | = | 2 | · | 2 | · | 2 | ||
| 14 | = | 2 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 7 | = | 7 | ||||||||
| 8 | = | 2 | · | 2 | · | 2 | ||||
| 14 | = | 2 | · | 7 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 7 | = | 56 |
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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