LCM( 378, 1080, 2890 ) = 2184840
Step 1: Write down factorisation of each number:
378 = 2 · 3 · 3 · 3 · 7
1080 = 2 · 2 · 2 · 3 · 3 · 3 · 5
2890 = 2 · 5 · 17 · 17
Step 2 : Match primes vertically:
378 | = | 2 | · | 3 | · | 3 | · | 3 | · | 7 | ||||||||||
1080 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 5 | ||||||
2890 | = | 2 | · | 5 | · | 17 | · | 17 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
378 | = | 2 | · | 3 | · | 3 | · | 3 | · | 7 | ||||||||||||
1080 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 5 | ||||||||
2890 | = | 2 | · | 5 | · | 17 | · | 17 | ||||||||||||||
LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 5 | · | 7 | · | 17 | · | 17 | = | 2184840 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.