Least Common Multiple (LCM) of 65 and 193
The least common multiple (LCM) of 65 and 193 is 12545.
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 65 and 193?
First, calculate the GCD of 65 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 193 = 0 remainder 65 |
| 2 | 193 ÷ 65 = 2 remainder 63 |
| 3 | 65 ÷ 63 = 1 remainder 2 |
| 4 | 63 ÷ 2 = 31 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 176 | 1584 |
| 169 and 102 | 17238 |
| 192 and 84 | 1344 |
| 115 and 187 | 21505 |
| 12 and 123 | 492 |