Least Common Multiple (LCM) of 170 and 195
The least common multiple (LCM) of 170 and 195 is 6630.
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 195?
First, calculate the GCD of 170 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 195 = 0 remainder 170 |
| 2 | 195 ÷ 170 = 1 remainder 25 |
| 3 | 170 ÷ 25 = 6 remainder 20 |
| 4 | 25 ÷ 20 = 1 remainder 5 |
| 5 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 60 | 3180 |
| 130 and 153 | 19890 |
| 165 and 71 | 11715 |
| 130 and 182 | 910 |
| 20 and 180 | 180 |