Least Common Multiple (LCM) of 121 and 180
The least common multiple (LCM) of 121 and 180 is 21780.
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 121 and 180?
First, calculate the GCD of 121 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 180 = 0 remainder 121 |
| 2 | 180 ÷ 121 = 1 remainder 59 |
| 3 | 121 ÷ 59 = 2 remainder 3 |
| 4 | 59 ÷ 3 = 19 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 129 | 5289 |
| 75 and 190 | 2850 |
| 194 and 129 | 25026 |
| 78 and 75 | 1950 |
| 28 and 78 | 1092 |