Least Common Multiple (LCM) of 50 and 107
The least common multiple (LCM) of 50 and 107 is 5350.
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 107?
First, calculate the GCD of 50 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 107 = 0 remainder 50 |
| 2 | 107 ÷ 50 = 2 remainder 7 |
| 3 | 50 ÷ 7 = 7 remainder 1 |
| 4 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 12 | 144 |
| 153 and 13 | 1989 |
| 84 and 32 | 672 |
| 129 and 41 | 5289 |
| 192 and 45 | 2880 |