Least Common Multiple (LCM) of 189 and 191
The least common multiple (LCM) of 189 and 191 is 36099.
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 189 and 191?
First, calculate the GCD of 189 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 191 = 0 remainder 189 |
| 2 | 191 ÷ 189 = 1 remainder 2 |
| 3 | 189 ÷ 2 = 94 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 74 | 14430 |
| 107 and 28 | 2996 |
| 198 and 111 | 7326 |
| 112 and 143 | 16016 |
| 171 and 104 | 17784 |