Least Common Multiple (LCM) of 50 and 122
The least common multiple (LCM) of 50 and 122 is 3050.
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 50 and 122?
First, calculate the GCD of 50 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 122 = 0 remainder 50 |
| 2 | 122 ÷ 50 = 2 remainder 22 |
| 3 | 50 ÷ 22 = 2 remainder 6 |
| 4 | 22 ÷ 6 = 3 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 18 | 990 |
| 139 and 74 | 10286 |
| 67 and 125 | 8375 |
| 27 and 39 | 351 |
| 150 and 92 | 6900 |