Least Common Multiple (LCM) of 85 and 194
The least common multiple (LCM) of 85 and 194 is 16490.
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 194?
First, calculate the GCD of 85 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 194 = 0 remainder 85 |
| 2 | 194 ÷ 85 = 2 remainder 24 |
| 3 | 85 ÷ 24 = 3 remainder 13 |
| 4 | 24 ÷ 13 = 1 remainder 11 |
| 5 | 13 ÷ 11 = 1 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 34 | 782 |
| 197 and 117 | 23049 |
| 160 and 172 | 6880 |
| 24 and 153 | 1224 |
| 54 and 156 | 1404 |