Least Common Multiple (LCM) of 180 and 122
The least common multiple (LCM) of 180 and 122 is 10980.
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 180 and 122?
First, calculate the GCD of 180 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 122 = 1 remainder 58 |
| 2 | 122 ÷ 58 = 2 remainder 6 |
| 3 | 58 ÷ 6 = 9 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 84 | 2856 |
| 82 and 59 | 4838 |
| 16 and 40 | 80 |
| 193 and 123 | 23739 |
| 42 and 51 | 714 |