LCM( 105, 90, 126 ) = 630
Step 1 : Place the numbers inside division bar:
105 | 90 | 126 |
Step 2 : Find a prime number which can divide at least two of your numbers.
In this example we can divide by 3. If any number is not divisible by 3 write it down unchanged.
3 | 105 | 90 | 126 |
35 | 30 | 42 |
Step 3 : Repeat Step 2 until you can no longer divide.
3 | 105 | 90 | 126 |
3 | 35 | 30 | 42 |
35 | 10 | 14 |
3 | 105 | 90 | 126 |
3 | 35 | 30 | 42 |
5 | 35 | 10 | 14 |
7 | 2 | 14 |
3 | 105 | 90 | 126 |
3 | 35 | 30 | 42 |
5 | 35 | 10 | 14 |
7 | 7 | 2 | 14 |
1 | 2 | 2 |
3 | 105 | 90 | 126 |
3 | 35 | 30 | 42 |
5 | 35 | 10 | 14 |
7 | 7 | 2 | 14 |
2 | 1 | 2 | 2 |
1 | 1 | 1 |
Since there are no primes that divides at least two of given numbers, we conclude that the LCM is a product of starting numbers.
LCM = 105 · 90 · 126 = 630
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.