Least Common Multiple (LCM) of 122 and 195
The least common multiple (LCM) of 122 and 195 is 23790.
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 195?
First, calculate the GCD of 122 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 195 = 0 remainder 122 |
| 2 | 195 ÷ 122 = 1 remainder 73 |
| 3 | 122 ÷ 73 = 1 remainder 49 |
| 4 | 73 ÷ 49 = 1 remainder 24 |
| 5 | 49 ÷ 24 = 2 remainder 1 |
| 6 | 24 ÷ 1 = 24 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 47 | 1551 |
| 189 and 195 | 12285 |
| 51 and 35 | 1785 |
| 61 and 135 | 8235 |
| 176 and 142 | 12496 |