Least Common Multiple (LCM) of 170 and 191
The least common multiple (LCM) of 170 and 191 is 32470.
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 191?
First, calculate the GCD of 170 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 191 = 0 remainder 170 |
| 2 | 191 ÷ 170 = 1 remainder 21 |
| 3 | 170 ÷ 21 = 8 remainder 2 |
| 4 | 21 ÷ 2 = 10 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 180 | 1980 |
| 84 and 165 | 4620 |
| 175 and 98 | 2450 |
| 178 and 63 | 11214 |
| 53 and 80 | 4240 |