Least Common Multiple (LCM) of 126 and 194
The least common multiple (LCM) of 126 and 194 is 12222.
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 126 and 194?
First, calculate the GCD of 126 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 194 = 0 remainder 126 |
| 2 | 194 ÷ 126 = 1 remainder 68 |
| 3 | 126 ÷ 68 = 1 remainder 58 |
| 4 | 68 ÷ 58 = 1 remainder 10 |
| 5 | 58 ÷ 10 = 5 remainder 8 |
| 6 | 10 ÷ 8 = 1 remainder 2 |
| 7 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 90 | 15210 |
| 185 and 188 | 34780 |
| 36 and 72 | 72 |
| 177 and 165 | 9735 |
| 193 and 85 | 16405 |