Least Common Multiple (LCM) of 122 and 185
The least common multiple (LCM) of 122 and 185 is 22570.
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 185?
First, calculate the GCD of 122 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 185 = 0 remainder 122 |
| 2 | 185 ÷ 122 = 1 remainder 63 |
| 3 | 122 ÷ 63 = 1 remainder 59 |
| 4 | 63 ÷ 59 = 1 remainder 4 |
| 5 | 59 ÷ 4 = 14 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 90 | 720 |
| 26 and 120 | 1560 |
| 87 and 29 | 87 |
| 52 and 104 | 104 |
| 42 and 196 | 588 |