Least Common Multiple (LCM) of 19 and 80
The least common multiple (LCM) of 19 and 80 is 1520.
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 19 and 80?
First, calculate the GCD of 19 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 80 = 0 remainder 19 |
| 2 | 80 ÷ 19 = 4 remainder 4 |
| 3 | 19 ÷ 4 = 4 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 85 | 10370 |
| 109 and 182 | 19838 |
| 158 and 112 | 8848 |
| 175 and 169 | 29575 |
| 179 and 182 | 32578 |