Least Common Multiple (LCM) of 172 and 185
The least common multiple (LCM) of 172 and 185 is 31820.
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 172 and 185?
First, calculate the GCD of 172 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 185 = 0 remainder 172 |
| 2 | 185 ÷ 172 = 1 remainder 13 |
| 3 | 172 ÷ 13 = 13 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 190 | 16910 |
| 177 and 89 | 15753 |
| 65 and 65 | 65 |
| 166 and 183 | 30378 |
| 180 and 146 | 13140 |