Find Least Common Multiple of 120, 210 and 225 using prime factorisation method.
Answer
LCM( 120, 210, 225 ) = 12600
Explanation
Step 1: Write down factorisation of each number:
120 = 2 · 2 · 2 · 3 · 5
210 = 2 · 3 · 5 · 7
225 = 3 · 3 · 5 · 5
Step 2 : Match primes vertically:
| 120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||||||
| 210 | = | 2 | · | 3 | · | 5 | · | 7 | ||||||||
| 225 | = | 3 | · | 3 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 120 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||||||||
| 210 | = | 2 | · | 3 | · | 5 | · | 7 | ||||||||||
| 225 | = | 3 | · | 3 | · | 5 | · | 5 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | · | 7 | = | 12600 |
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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