Least Common Multiple (LCM) of 180 and 173
The least common multiple (LCM) of 180 and 173 is 31140.
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 173?
First, calculate the GCD of 180 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 173 = 1 remainder 7 |
| 2 | 173 ÷ 7 = 24 remainder 5 |
| 3 | 7 ÷ 5 = 1 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 172 | 3440 |
| 84 and 100 | 2100 |
| 89 and 140 | 12460 |
| 143 and 174 | 24882 |
| 58 and 27 | 1566 |