Find Least Common Multiple of 625, 225 and 215 using prime factorisation method.
Answer
LCM( 625, 225, 215 ) = 241875
Explanation
Step 1: Write down factorisation of each number:
625 = 5 · 5 · 5 · 5
225 = 3 · 3 · 5 · 5
215 = 5 · 43
Step 2 : Match primes vertically:
| 625 | = | 5 | · | 5 | · | 5 | · | 5 | ||||||
| 225 | = | 3 | · | 3 | · | 5 | · | 5 | ||||||
| 215 | = | 5 | · | 43 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 625 | = | 5 | · | 5 | · | 5 | · | 5 | ||||||||
| 225 | = | 3 | · | 3 | · | 5 | · | 5 | ||||||||
| 215 | = | 5 | · | 43 | ||||||||||||
| LCM | = | 3 | · | 3 | · | 5 | · | 5 | · | 5 | · | 5 | · | 43 | = | 241875 |
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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