Least Common Multiple (LCM) of 67 and 50
The least common multiple (LCM) of 67 and 50 is 3350.
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 67 and 50?
First, calculate the GCD of 67 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 50 = 1 remainder 17 |
| 2 | 50 ÷ 17 = 2 remainder 16 |
| 3 | 17 ÷ 16 = 1 remainder 1 |
| 4 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 11 | 110 |
| 155 and 67 | 10385 |
| 92 and 10 | 460 |
| 191 and 185 | 35335 |
| 15 and 13 | 195 |