Least Common Multiple (LCM) of 199 and 189
The least common multiple (LCM) of 199 and 189 is 37611.
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 199 and 189?
First, calculate the GCD of 199 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 189 = 1 remainder 10 |
| 2 | 189 ÷ 10 = 18 remainder 9 |
| 3 | 10 ÷ 9 = 1 remainder 1 |
| 4 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 66 | 330 |
| 115 and 97 | 11155 |
| 74 and 110 | 4070 |
| 120 and 138 | 2760 |
| 18 and 105 | 630 |