Least Common Multiple (LCM) of 193 and 68
The least common multiple (LCM) of 193 and 68 is 13124.
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 193 and 68?
First, calculate the GCD of 193 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 68 = 2 remainder 57 |
| 2 | 68 ÷ 57 = 1 remainder 11 |
| 3 | 57 ÷ 11 = 5 remainder 2 |
| 4 | 11 ÷ 2 = 5 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 102 | 17850 |
| 125 and 16 | 2000 |
| 191 and 127 | 24257 |
| 82 and 154 | 6314 |
| 177 and 56 | 9912 |