Least Common Multiple (LCM) of 103 and 50
The least common multiple (LCM) of 103 and 50 is 5150.
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 103 and 50?
First, calculate the GCD of 103 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 50 = 2 remainder 3 |
| 2 | 50 ÷ 3 = 16 remainder 2 |
| 3 | 3 ÷ 2 = 1 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 10 | 1990 |
| 14 and 174 | 1218 |
| 146 and 142 | 10366 |
| 31 and 114 | 3534 |
| 19 and 104 | 1976 |