Least Common Multiple (LCM) of 85 and 197
The least common multiple (LCM) of 85 and 197 is 16745.
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 197?
First, calculate the GCD of 85 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 197 = 0 remainder 85 |
| 2 | 197 ÷ 85 = 2 remainder 27 |
| 3 | 85 ÷ 27 = 3 remainder 4 |
| 4 | 27 ÷ 4 = 6 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 132 | 2112 |
| 129 and 102 | 4386 |
| 68 and 145 | 9860 |
| 63 and 14 | 126 |
| 160 and 31 | 4960 |