Least Common Multiple (LCM) of 50 and 137
The least common multiple (LCM) of 50 and 137 is 6850.
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 137?
First, calculate the GCD of 50 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 137 = 0 remainder 50 |
| 2 | 137 ÷ 50 = 2 remainder 37 |
| 3 | 50 ÷ 37 = 1 remainder 13 |
| 4 | 37 ÷ 13 = 2 remainder 11 |
| 5 | 13 ÷ 11 = 1 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 48 | 7152 |
| 161 and 197 | 31717 |
| 37 and 77 | 2849 |
| 179 and 166 | 29714 |
| 97 and 80 | 7760 |