Least Common Multiple (LCM) of 189 and 103
The least common multiple (LCM) of 189 and 103 is 19467.
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 103?
First, calculate the GCD of 189 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 103 = 1 remainder 86 |
| 2 | 103 ÷ 86 = 1 remainder 17 |
| 3 | 86 ÷ 17 = 5 remainder 1 |
| 4 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 183 | 2745 |
| 125 and 55 | 1375 |
| 158 and 178 | 14062 |
| 138 and 188 | 12972 |
| 165 and 166 | 27390 |