Least Common Multiple (LCM) of 109 and 193
The least common multiple (LCM) of 109 and 193 is 21037.
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 193?
First, calculate the GCD of 109 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 193 = 0 remainder 109 |
| 2 | 193 ÷ 109 = 1 remainder 84 |
| 3 | 109 ÷ 84 = 1 remainder 25 |
| 4 | 84 ÷ 25 = 3 remainder 9 |
| 5 | 25 ÷ 9 = 2 remainder 7 |
| 6 | 9 ÷ 7 = 1 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 77 | 10934 |
| 149 and 17 | 2533 |
| 141 and 107 | 15087 |
| 142 and 48 | 3408 |
| 150 and 149 | 22350 |