Least Common Multiple (LCM) of 122 and 85
The least common multiple (LCM) of 122 and 85 is 10370.
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 85?
First, calculate the GCD of 122 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 85 = 1 remainder 37 |
| 2 | 85 ÷ 37 = 2 remainder 11 |
| 3 | 37 ÷ 11 = 3 remainder 4 |
| 4 | 11 ÷ 4 = 2 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 135 | 3105 |
| 148 and 71 | 10508 |
| 82 and 156 | 6396 |
| 47 and 114 | 5358 |
| 35 and 106 | 3710 |