Least Common Multiple (LCM) of 125 and 197
The least common multiple (LCM) of 125 and 197 is 24625.
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 125 and 197?
First, calculate the GCD of 125 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 197 = 0 remainder 125 |
| 2 | 197 ÷ 125 = 1 remainder 72 |
| 3 | 125 ÷ 72 = 1 remainder 53 |
| 4 | 72 ÷ 53 = 1 remainder 19 |
| 5 | 53 ÷ 19 = 2 remainder 15 |
| 6 | 19 ÷ 15 = 1 remainder 4 |
| 7 | 15 ÷ 4 = 3 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 166 | 20750 |
| 119 and 145 | 17255 |
| 164 and 45 | 7380 |
| 81 and 20 | 1620 |
| 197 and 76 | 14972 |