Least Common Multiple (LCM) of 180 and 85
The least common multiple (LCM) of 180 and 85 is 3060.
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 180 and 85?
First, calculate the GCD of 180 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 85 = 2 remainder 10 |
| 2 | 85 ÷ 10 = 8 remainder 5 |
| 3 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 173 | 5363 |
| 118 and 109 | 12862 |
| 167 and 34 | 5678 |
| 172 and 186 | 15996 |
| 100 and 78 | 3900 |