Least Common Multiple (LCM) of 80 and 195
The least common multiple (LCM) of 80 and 195 is 3120.
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 80 and 195?
First, calculate the GCD of 80 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 195 = 0 remainder 80 |
| 2 | 195 ÷ 80 = 2 remainder 35 |
| 3 | 80 ÷ 35 = 2 remainder 10 |
| 4 | 35 ÷ 10 = 3 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 165 | 9735 |
| 39 and 75 | 975 |
| 70 and 78 | 2730 |
| 150 and 126 | 3150 |
| 170 and 30 | 510 |