LCM( 72, 80, 252 ) = 5040
Step 1 : Place the numbers inside division bar:
72 | 80 | 252 |
Step 2 : Find a prime number which can divide at least two of your numbers.
In this example we can divide by 2. If any number is not divisible by 2 write it down unchanged.
2 | 72 | 80 | 252 |
36 | 40 | 126 |
Step 3 : Repeat Step 2 until you can no longer divide.
2 | 72 | 80 | 252 |
2 | 36 | 40 | 126 |
18 | 20 | 63 |
2 | 72 | 80 | 252 |
2 | 36 | 40 | 126 |
2 | 18 | 20 | 63 |
9 | 10 | 63 |
2 | 72 | 80 | 252 |
2 | 36 | 40 | 126 |
2 | 18 | 20 | 63 |
3 | 9 | 10 | 63 |
3 | 10 | 21 |
2 | 72 | 80 | 252 |
2 | 36 | 40 | 126 |
2 | 18 | 20 | 63 |
3 | 9 | 10 | 63 |
3 | 3 | 10 | 21 |
1 | 10 | 7 |
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 = 72 · 80 · 252 = 5040
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.