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 |
|---|---|
| 184 and 53 | 9752 |
| 54 and 91 | 4914 |
| 141 and 22 | 3102 |
| 15 and 77 | 1155 |
| 178 and 187 | 33286 |