Least Common Multiple (LCM) of 122 and 193
The least common multiple (LCM) of 122 and 193 is 23546.
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 193?
First, calculate the GCD of 122 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 193 = 0 remainder 122 |
| 2 | 193 ÷ 122 = 1 remainder 71 |
| 3 | 122 ÷ 71 = 1 remainder 51 |
| 4 | 71 ÷ 51 = 1 remainder 20 |
| 5 | 51 ÷ 20 = 2 remainder 11 |
| 6 | 20 ÷ 11 = 1 remainder 9 |
| 7 | 11 ÷ 9 = 1 remainder 2 |
| 8 | 9 ÷ 2 = 4 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 133 | 14497 |
| 104 and 75 | 7800 |
| 48 and 89 | 4272 |
| 170 and 29 | 4930 |
| 142 and 131 | 18602 |