Least Common Multiple (LCM) of 191 and 71
The least common multiple (LCM) of 191 and 71 is 13561.
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 71?
First, calculate the GCD of 191 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 191 ÷ 71 = 2 remainder 49 |
| 2 | 71 ÷ 49 = 1 remainder 22 |
| 3 | 49 ÷ 22 = 2 remainder 5 |
| 4 | 22 ÷ 5 = 4 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 175 | 525 |
| 197 and 37 | 7289 |
| 66 and 118 | 3894 |
| 72 and 22 | 792 |
| 55 and 198 | 990 |