Least Common Multiple (LCM) of 197 and 170
The least common multiple (LCM) of 197 and 170 is 33490.
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 197 and 170?
First, calculate the GCD of 197 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 170 = 1 remainder 27 |
| 2 | 170 ÷ 27 = 6 remainder 8 |
| 3 | 27 ÷ 8 = 3 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 185 | 12765 |
| 186 and 174 | 5394 |
| 84 and 175 | 2100 |
| 107 and 176 | 18832 |
| 14 and 96 | 672 |