Least Common Multiple (LCM) of 127 and 197
The least common multiple (LCM) of 127 and 197 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 127 and 197?
First, calculate the GCD of 127 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 197 = 0 remainder 127 |
| 2 | 197 ÷ 127 = 1 remainder 70 |
| 3 | 127 ÷ 70 = 1 remainder 57 |
| 4 | 70 ÷ 57 = 1 remainder 13 |
| 5 | 57 ÷ 13 = 4 remainder 5 |
| 6 | 13 ÷ 5 = 2 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 51 | 4947 |
| 186 and 170 | 15810 |
| 25 and 123 | 3075 |
| 40 and 104 | 520 |
| 140 and 64 | 2240 |