Least Common Multiple (LCM) of 185 and 171
The least common multiple (LCM) of 185 and 171 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 185 and 171?
First, calculate the GCD of 185 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 171 = 1 remainder 14 |
| 2 | 171 ÷ 14 = 12 remainder 3 |
| 3 | 14 ÷ 3 = 4 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 100 | 700 |
| 13 and 93 | 1209 |
| 132 and 26 | 1716 |
| 72 and 147 | 3528 |
| 97 and 173 | 16781 |