Least Common Multiple (LCM) of 199 and 80
The least common multiple (LCM) of 199 and 80 is 15920.
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 199 and 80?
First, calculate the GCD of 199 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 80 = 2 remainder 39 |
| 2 | 80 ÷ 39 = 2 remainder 2 |
| 3 | 39 ÷ 2 = 19 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 63 | 1575 |
| 105 and 33 | 1155 |
| 193 and 110 | 21230 |
| 187 and 50 | 9350 |
| 23 and 89 | 2047 |