Question
Find Least Common Multiple of 21, 35 and 425 using prime factorisation method.
Answer
LCM( 21, 35, 425 ) = 8925
Explanation
Step 1: Write down factorisation of each number:
21 = 3 · 7
35 = 5 · 7
425 = 5 · 5 · 17
Step 2 : Match primes vertically:
| 21 | = | 3 | · | 7 | ||||||
| 35 | = | 5 | · | 7 | ||||||
| 425 | = | 5 | · | 5 | · | 17 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 21 | = | 3 | · | 7 | ||||||||
| 35 | = | 5 | · | 7 | ||||||||
| 425 | = | 5 | · | 5 | · | 17 | ||||||
| LCM | = | 3 | · | 5 | · | 5 | · | 7 | · | 17 | = | 8925 |
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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