Least Common Multiple (LCM) of 191 and 116
The least common multiple (LCM) of 191 and 116 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 191 and 116?
First, calculate the GCD of 191 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 191 ÷ 116 = 1 remainder 75 |
| 2 | 116 ÷ 75 = 1 remainder 41 |
| 3 | 75 ÷ 41 = 1 remainder 34 |
| 4 | 41 ÷ 34 = 1 remainder 7 |
| 5 | 34 ÷ 7 = 4 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 110 | 5720 |
| 130 and 116 | 7540 |
| 106 and 116 | 6148 |
| 192 and 69 | 4416 |
| 194 and 81 | 15714 |