Least Common Multiple (LCM) of 197 and 116
The least common multiple (LCM) of 197 and 116 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 197 and 116?
First, calculate the GCD of 197 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 116 = 1 remainder 81 |
| 2 | 116 ÷ 81 = 1 remainder 35 |
| 3 | 81 ÷ 35 = 2 remainder 11 |
| 4 | 35 ÷ 11 = 3 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 80 | 9520 |
| 47 and 111 | 5217 |
| 110 and 114 | 6270 |
| 52 and 161 | 8372 |
| 57 and 177 | 3363 |