Least Common Multiple (LCM) of 67 and 180
The least common multiple (LCM) of 67 and 180 is 12060.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 67 and 180?
First, calculate the GCD of 67 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 180 = 0 remainder 67 |
| 2 | 180 ÷ 67 = 2 remainder 46 |
| 3 | 67 ÷ 46 = 1 remainder 21 |
| 4 | 46 ÷ 21 = 2 remainder 4 |
| 5 | 21 ÷ 4 = 5 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 81 | 324 |
| 162 and 172 | 13932 |
| 66 and 86 | 2838 |
| 186 and 37 | 6882 |
| 24 and 71 | 1704 |