Least Common Multiple (LCM) of 171 and 191
The least common multiple (LCM) of 171 and 191 is 32661.
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 171 and 191?
First, calculate the GCD of 171 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 191 = 0 remainder 171 |
| 2 | 191 ÷ 171 = 1 remainder 20 |
| 3 | 171 ÷ 20 = 8 remainder 11 |
| 4 | 20 ÷ 11 = 1 remainder 9 |
| 5 | 11 ÷ 9 = 1 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 77 | 2464 |
| 102 and 91 | 9282 |
| 48 and 96 | 96 |
| 51 and 41 | 2091 |
| 105 and 153 | 5355 |