Least Common Multiple (LCM) of 128 and 193
The least common multiple (LCM) of 128 and 193 is 24704.
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 128 and 193?
First, calculate the GCD of 128 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 193 = 0 remainder 128 |
| 2 | 193 ÷ 128 = 1 remainder 65 |
| 3 | 128 ÷ 65 = 1 remainder 63 |
| 4 | 65 ÷ 63 = 1 remainder 2 |
| 5 | 63 ÷ 2 = 31 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 109 | 20601 |
| 189 and 136 | 25704 |
| 181 and 115 | 20815 |
| 72 and 115 | 8280 |
| 103 and 95 | 9785 |