Find Least Common Multiple of 3020, 2835 and 3125 using prime factorisation method.
Answer
LCM( 3020, 2835, 3125 ) = 1070212500
Explanation
Step 1: Write down factorisation of each number:
3020 = 2 · 2 · 5 · 151
2835 = 3 · 3 · 3 · 3 · 5 · 7
3125 = 5 · 5 · 5 · 5 · 5
Step 2 : Match primes vertically:
| 3020 | = | 2 | · | 2 | · | 5 | · | 151 | ||||||||||||||||||
| 2835 | = | 3 | · | 3 | · | 3 | · | 3 | · | 5 | · | 7 | ||||||||||||||
| 3125 | = | 5 | · | 5 | · | 5 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 3020 | = | 2 | · | 2 | · | 5 | · | 151 | ||||||||||||||||||||
| 2835 | = | 3 | · | 3 | · | 3 | · | 3 | · | 5 | · | 7 | ||||||||||||||||
| 3125 | = | 5 | · | 5 | · | 5 | · | 5 | · | 5 | ||||||||||||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 3 | · | 5 | · | 5 | · | 5 | · | 5 | · | 5 | · | 7 | · | 151 | = | 1070212500 |
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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