Least Common Multiple (LCM) of 122 and 180
The least common multiple (LCM) of 122 and 180 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 122 and 180?
First, calculate the GCD of 122 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 180 = 0 remainder 122 |
| 2 | 180 ÷ 122 = 1 remainder 58 |
| 3 | 122 ÷ 58 = 2 remainder 6 |
| 4 | 58 ÷ 6 = 9 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 179 | 23449 |
| 146 and 24 | 1752 |
| 105 and 152 | 15960 |
| 143 and 84 | 12012 |
| 84 and 103 | 8652 |