Least Common Multiple (LCM) of 38 and 193
The least common multiple (LCM) of 38 and 193 is 7334.
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 38 and 193?
First, calculate the GCD of 38 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 193 = 0 remainder 38 |
| 2 | 193 ÷ 38 = 5 remainder 3 |
| 3 | 38 ÷ 3 = 12 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 120 | 15720 |
| 52 and 172 | 2236 |
| 188 and 91 | 17108 |
| 142 and 145 | 20590 |
| 155 and 25 | 775 |