Least Common Multiple (LCM) of 113 and 197
The least common multiple (LCM) of 113 and 197 is 22261.
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 113 and 197?
First, calculate the GCD of 113 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 197 = 0 remainder 113 |
| 2 | 197 ÷ 113 = 1 remainder 84 |
| 3 | 113 ÷ 84 = 1 remainder 29 |
| 4 | 84 ÷ 29 = 2 remainder 26 |
| 5 | 29 ÷ 26 = 1 remainder 3 |
| 6 | 26 ÷ 3 = 8 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 15 | 75 |
| 35 and 145 | 1015 |
| 37 and 116 | 4292 |
| 89 and 99 | 8811 |
| 65 and 142 | 9230 |