Question
Find Least Common Multiple of 25, 125 and 625 using prime factorisation method.
Answer
LCM( 25, 125, 625 ) = 625
Explanation
Step 1: Write down factorisation of each number:
25 = 5 · 5
125 = 5 · 5 · 5
625 = 5 · 5 · 5 · 5
Step 2 : Match primes vertically:
| 25 | = | 5 | · | 5 | ||||
| 125 | = | 5 | · | 5 | · | 5 | ||
| 625 | = | 5 | · | 5 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 25 | = | 5 | · | 5 | ||||||
| 125 | = | 5 | · | 5 | · | 5 | ||||
| 625 | = | 5 | · | 5 | · | 5 | · | 5 | ||
| LCM | = | 5 | · | 5 | · | 5 | · | 5 | = | 625 |
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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