Least Common Multiple (LCM) of 77 and 180
The least common multiple (LCM) of 77 and 180 is 13860.
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 77 and 180?
First, calculate the GCD of 77 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 180 = 0 remainder 77 |
| 2 | 180 ÷ 77 = 2 remainder 26 |
| 3 | 77 ÷ 26 = 2 remainder 25 |
| 4 | 26 ÷ 25 = 1 remainder 1 |
| 5 | 25 ÷ 1 = 25 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 40 | 200 |
| 144 and 85 | 12240 |
| 164 and 125 | 20500 |
| 197 and 149 | 29353 |
| 196 and 81 | 15876 |