Least Common Multiple (LCM) of 171 and 185
The least common multiple (LCM) of 171 and 185 is 31635.
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 185?
First, calculate the GCD of 171 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 185 = 0 remainder 171 |
| 2 | 185 ÷ 171 = 1 remainder 14 |
| 3 | 171 ÷ 14 = 12 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 28 | 140 |
| 24 and 192 | 192 |
| 48 and 15 | 240 |
| 104 and 13 | 104 |
| 35 and 80 | 560 |