Least Common Multiple (LCM) of 193 and 109
The least common multiple (LCM) of 193 and 109 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 193 and 109?
First, calculate the GCD of 193 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 109 = 1 remainder 84 |
| 2 | 109 ÷ 84 = 1 remainder 25 |
| 3 | 84 ÷ 25 = 3 remainder 9 |
| 4 | 25 ÷ 9 = 2 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 182 | 910 |
| 32 and 158 | 2528 |
| 38 and 120 | 2280 |
| 109 and 156 | 17004 |
| 163 and 134 | 21842 |