Least Common Multiple (LCM) of 80 and 193
The least common multiple (LCM) of 80 and 193 is 15440.
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 193?
First, calculate the GCD of 80 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 193 = 0 remainder 80 |
| 2 | 193 ÷ 80 = 2 remainder 33 |
| 3 | 80 ÷ 33 = 2 remainder 14 |
| 4 | 33 ÷ 14 = 2 remainder 5 |
| 5 | 14 ÷ 5 = 2 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 110 | 21230 |
| 163 and 112 | 18256 |
| 148 and 11 | 1628 |
| 147 and 196 | 588 |
| 80 and 160 | 160 |