Least Common Multiple (LCM) of 170 and 197
The least common multiple (LCM) of 170 and 197 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 170 and 197?
First, calculate the GCD of 170 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 197 = 0 remainder 170 |
| 2 | 197 ÷ 170 = 1 remainder 27 |
| 3 | 170 ÷ 27 = 6 remainder 8 |
| 4 | 27 ÷ 8 = 3 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 109 | 12862 |
| 145 and 58 | 290 |
| 193 and 35 | 6755 |
| 71 and 123 | 8733 |
| 168 and 39 | 2184 |