Least Common Multiple (LCM) of 80 and 198
The least common multiple (LCM) of 80 and 198 is 7920.
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 198?
First, calculate the GCD of 80 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 198 = 0 remainder 80 |
| 2 | 198 ÷ 80 = 2 remainder 38 |
| 3 | 80 ÷ 38 = 2 remainder 4 |
| 4 | 38 ÷ 4 = 9 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 88 | 4136 |
| 60 and 90 | 180 |
| 130 and 107 | 13910 |
| 83 and 139 | 11537 |
| 190 and 145 | 5510 |