Least Common Multiple (LCM) of 130 and 193
The least common multiple (LCM) of 130 and 193 is 25090.
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 130 and 193?
First, calculate the GCD of 130 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 193 = 0 remainder 130 |
| 2 | 193 ÷ 130 = 1 remainder 63 |
| 3 | 130 ÷ 63 = 2 remainder 4 |
| 4 | 63 ÷ 4 = 15 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 80 | 400 |
| 19 and 79 | 1501 |
| 135 and 199 | 26865 |
| 129 and 107 | 13803 |
| 71 and 65 | 4615 |