Least Common Multiple (LCM) of 109 and 181
The least common multiple (LCM) of 109 and 181 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 109 and 181?
First, calculate the GCD of 109 and 181 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 181 = 0 remainder 109 |
| 2 | 181 ÷ 109 = 1 remainder 72 |
| 3 | 109 ÷ 72 = 1 remainder 37 |
| 4 | 72 ÷ 37 = 1 remainder 35 |
| 5 | 37 ÷ 35 = 1 remainder 2 |
| 6 | 35 ÷ 2 = 17 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 82 | 3444 |
| 54 and 40 | 1080 |
| 63 and 192 | 4032 |
| 125 and 171 | 21375 |
| 94 and 37 | 3478 |