Least Common Multiple (LCM) of 177 and 194
The least common multiple (LCM) of 177 and 194 is 34338.
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 177 and 194?
First, calculate the GCD of 177 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 194 = 0 remainder 177 |
| 2 | 194 ÷ 177 = 1 remainder 17 |
| 3 | 177 ÷ 17 = 10 remainder 7 |
| 4 | 17 ÷ 7 = 2 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 34 | 6426 |
| 184 and 22 | 2024 |
| 142 and 152 | 10792 |
| 173 and 35 | 6055 |
| 36 and 108 | 108 |