Least Common Multiple (LCM) of 189 and 199
The least common multiple (LCM) of 189 and 199 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 189 and 199?
First, calculate the GCD of 189 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 199 = 0 remainder 189 |
| 2 | 199 ÷ 189 = 1 remainder 10 |
| 3 | 189 ÷ 10 = 18 remainder 9 |
| 4 | 10 ÷ 9 = 1 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 174 | 3306 |
| 74 and 82 | 3034 |
| 109 and 59 | 6431 |
| 194 and 88 | 8536 |
| 114 and 52 | 2964 |