Least Common Multiple (LCM) of 116 and 197
The least common multiple (LCM) of 116 and 197 is 22852.
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 116 and 197?
First, calculate the GCD of 116 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 197 = 0 remainder 116 |
| 2 | 197 ÷ 116 = 1 remainder 81 |
| 3 | 116 ÷ 81 = 1 remainder 35 |
| 4 | 81 ÷ 35 = 2 remainder 11 |
| 5 | 35 ÷ 11 = 3 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 131 | 10742 |
| 151 and 31 | 4681 |
| 75 and 110 | 1650 |
| 48 and 165 | 2640 |
| 45 and 61 | 2745 |