Least Common Multiple (LCM) of 188 and 193
The least common multiple (LCM) of 188 and 193 is 36284.
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 188 and 193?
First, calculate the GCD of 188 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 193 = 0 remainder 188 |
| 2 | 193 ÷ 188 = 1 remainder 5 |
| 3 | 188 ÷ 5 = 37 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 161 | 22057 |
| 26 and 74 | 962 |
| 127 and 91 | 11557 |
| 165 and 158 | 26070 |
| 191 and 102 | 19482 |