LCM( 75, 40, 90 ) = 1800
Step 1 : Place the numbers inside division bar:
75 | 40 | 90 |
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 | 75 | 40 | 90 |
25 | 40 | 30 |
Step 3 : Repeat Step 2 until you can no longer divide.
3 | 75 | 40 | 90 |
5 | 25 | 40 | 30 |
5 | 8 | 6 |
3 | 75 | 40 | 90 |
5 | 25 | 40 | 30 |
2 | 5 | 8 | 6 |
5 | 4 | 3 |
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 = 75 · 40 · 90 = 1800
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.