Least Common Multiple (LCM) of 189 and 181
The least common multiple (LCM) of 189 and 181 is 34209.
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 181?
First, calculate the GCD of 189 and 181 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 181 = 1 remainder 8 |
| 2 | 181 ÷ 8 = 22 remainder 5 |
| 3 | 8 ÷ 5 = 1 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 28 | 700 |
| 142 and 166 | 11786 |
| 148 and 122 | 9028 |
| 151 and 109 | 16459 |
| 177 and 84 | 4956 |