Least Common Multiple (LCM) of 80 and 199
The least common multiple (LCM) of 80 and 199 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 80 and 199?
First, calculate the GCD of 80 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 199 = 0 remainder 80 |
| 2 | 199 ÷ 80 = 2 remainder 39 |
| 3 | 80 ÷ 39 = 2 remainder 2 |
| 4 | 39 ÷ 2 = 19 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 53 | 7208 |
| 33 and 47 | 1551 |
| 144 and 192 | 576 |
| 164 and 178 | 14596 |
| 122 and 191 | 23302 |