Least Common Multiple (LCM) of 126 and 197
The least common multiple (LCM) of 126 and 197 is 24822.
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 197?
First, calculate the GCD of 126 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 197 = 0 remainder 126 |
| 2 | 197 ÷ 126 = 1 remainder 71 |
| 3 | 126 ÷ 71 = 1 remainder 55 |
| 4 | 71 ÷ 55 = 1 remainder 16 |
| 5 | 55 ÷ 16 = 3 remainder 7 |
| 6 | 16 ÷ 7 = 2 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 120 | 240 |
| 185 and 55 | 2035 |
| 173 and 44 | 7612 |
| 194 and 119 | 23086 |
| 63 and 185 | 11655 |