Least Common Multiple (LCM) of 85 and 193
The least common multiple (LCM) of 85 and 193 is 16405.
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 85 and 193?
First, calculate the GCD of 85 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 193 = 0 remainder 85 |
| 2 | 193 ÷ 85 = 2 remainder 23 |
| 3 | 85 ÷ 23 = 3 remainder 16 |
| 4 | 23 ÷ 16 = 1 remainder 7 |
| 5 | 16 ÷ 7 = 2 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 145 | 15805 |
| 91 and 168 | 2184 |
| 168 and 15 | 840 |
| 60 and 74 | 2220 |
| 87 and 45 | 1305 |