Least Common Multiple (LCM) of 85 and 185
The least common multiple (LCM) of 85 and 185 is 3145.
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 185?
First, calculate the GCD of 85 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 185 = 0 remainder 85 |
| 2 | 185 ÷ 85 = 2 remainder 15 |
| 3 | 85 ÷ 15 = 5 remainder 10 |
| 4 | 15 ÷ 10 = 1 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 162 | 810 |
| 30 and 199 | 5970 |
| 166 and 177 | 29382 |
| 89 and 196 | 17444 |
| 60 and 105 | 420 |