Least Common Multiple (LCM) of 50 and 109
The least common multiple (LCM) of 50 and 109 is 5450.
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 109?
First, calculate the GCD of 50 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 109 = 0 remainder 50 |
| 2 | 109 ÷ 50 = 2 remainder 9 |
| 3 | 50 ÷ 9 = 5 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 174 | 30450 |
| 85 and 114 | 9690 |
| 199 and 164 | 32636 |
| 196 and 144 | 7056 |
| 146 and 86 | 6278 |