Least Common Multiple (LCM) of 50 and 121
The least common multiple (LCM) of 50 and 121 is 6050.
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 121?
First, calculate the GCD of 50 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 121 = 0 remainder 50 |
| 2 | 121 ÷ 50 = 2 remainder 21 |
| 3 | 50 ÷ 21 = 2 remainder 8 |
| 4 | 21 ÷ 8 = 2 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 101 | 1818 |
| 196 and 144 | 7056 |
| 128 and 125 | 16000 |
| 159 and 99 | 5247 |
| 101 and 114 | 11514 |