Least Common Multiple (LCM) of 19 and 189
The least common multiple (LCM) of 19 and 189 is 3591.
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 19 and 189?
First, calculate the GCD of 19 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 189 = 0 remainder 19 |
| 2 | 189 ÷ 19 = 9 remainder 18 |
| 3 | 19 ÷ 18 = 1 remainder 1 |
| 4 | 18 ÷ 1 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 146 | 8176 |
| 199 and 142 | 28258 |
| 23 and 14 | 322 |
| 105 and 84 | 420 |
| 166 and 172 | 14276 |