Least Common Multiple (LCM) of 122 and 194
The least common multiple (LCM) of 122 and 194 is 11834.
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 194?
First, calculate the GCD of 122 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 194 = 0 remainder 122 |
| 2 | 194 ÷ 122 = 1 remainder 72 |
| 3 | 122 ÷ 72 = 1 remainder 50 |
| 4 | 72 ÷ 50 = 1 remainder 22 |
| 5 | 50 ÷ 22 = 2 remainder 6 |
| 6 | 22 ÷ 6 = 3 remainder 4 |
| 7 | 6 ÷ 4 = 1 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 156 | 156 |
| 162 and 78 | 2106 |
| 35 and 173 | 6055 |
| 116 and 68 | 1972 |
| 171 and 139 | 23769 |