Least Common Multiple (LCM) of 116 and 191
The least common multiple (LCM) of 116 and 191 is 22156.
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 191?
First, calculate the GCD of 116 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 191 = 0 remainder 116 |
| 2 | 191 ÷ 116 = 1 remainder 75 |
| 3 | 116 ÷ 75 = 1 remainder 41 |
| 4 | 75 ÷ 41 = 1 remainder 34 |
| 5 | 41 ÷ 34 = 1 remainder 7 |
| 6 | 34 ÷ 7 = 4 remainder 6 |
| 7 | 7 ÷ 6 = 1 remainder 1 |
| 8 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 38 | 418 |
| 195 and 122 | 23790 |
| 156 and 103 | 16068 |
| 62 and 33 | 2046 |
| 180 and 119 | 21420 |