Least Common Multiple (LCM) of 181 and 109
The least common multiple (LCM) of 181 and 109 is 19729.
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 181 and 109?
First, calculate the GCD of 181 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 181 ÷ 109 = 1 remainder 72 |
| 2 | 109 ÷ 72 = 1 remainder 37 |
| 3 | 72 ÷ 37 = 1 remainder 35 |
| 4 | 37 ÷ 35 = 1 remainder 2 |
| 5 | 35 ÷ 2 = 17 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 75 | 2175 |
| 193 and 71 | 13703 |
| 74 and 199 | 14726 |
| 10 and 97 | 970 |
| 20 and 122 | 1220 |