Least Common Multiple (LCM) of 13 and 194
The least common multiple (LCM) of 13 and 194 is 2522.
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 13 and 194?
First, calculate the GCD of 13 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 194 = 0 remainder 13 |
| 2 | 194 ÷ 13 = 14 remainder 12 |
| 3 | 13 ÷ 12 = 1 remainder 1 |
| 4 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 109 | 5995 |
| 159 and 91 | 14469 |
| 33 and 103 | 3399 |
| 136 and 199 | 27064 |
| 39 and 153 | 1989 |