Least Common Multiple (LCM) of 197 and 127
The least common multiple (LCM) of 197 and 127 is 25019.
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 197 and 127?
First, calculate the GCD of 197 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 127 = 1 remainder 70 |
| 2 | 127 ÷ 70 = 1 remainder 57 |
| 3 | 70 ÷ 57 = 1 remainder 13 |
| 4 | 57 ÷ 13 = 4 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 45 | 6390 |
| 60 and 178 | 5340 |
| 109 and 115 | 12535 |
| 154 and 119 | 2618 |
| 185 and 165 | 6105 |