Least Common Multiple (LCM) of 80 and 135
The least common multiple (LCM) of 80 and 135 is 2160.
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 135?
First, calculate the GCD of 80 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 135 = 0 remainder 80 |
| 2 | 135 ÷ 80 = 1 remainder 55 |
| 3 | 80 ÷ 55 = 1 remainder 25 |
| 4 | 55 ÷ 25 = 2 remainder 5 |
| 5 | 25 ÷ 5 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 34 | 1938 |
| 132 and 195 | 8580 |
| 103 and 29 | 2987 |
| 130 and 118 | 7670 |
| 135 and 51 | 2295 |