Least Common Multiple (LCM) of 127 and 196
The least common multiple (LCM) of 127 and 196 is 24892.
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 127 and 196?
First, calculate the GCD of 127 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 196 = 0 remainder 127 |
| 2 | 196 ÷ 127 = 1 remainder 69 |
| 3 | 127 ÷ 69 = 1 remainder 58 |
| 4 | 69 ÷ 58 = 1 remainder 11 |
| 5 | 58 ÷ 11 = 5 remainder 3 |
| 6 | 11 ÷ 3 = 3 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 137 | 13837 |
| 172 and 12 | 516 |
| 20 and 22 | 220 |
| 195 and 38 | 7410 |
| 185 and 125 | 4625 |