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 |
|---|---|
| 160 and 60 | 480 |
| 10 and 113 | 1130 |
| 74 and 102 | 3774 |
| 191 and 41 | 7831 |
| 170 and 75 | 2550 |