Least Common Multiple (LCM) of 135 and 80
The least common multiple (LCM) of 135 and 80 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 135 and 80?
First, calculate the GCD of 135 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 80 = 1 remainder 55 |
| 2 | 80 ÷ 55 = 1 remainder 25 |
| 3 | 55 ÷ 25 = 2 remainder 5 |
| 4 | 25 ÷ 5 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 146 | 4818 |
| 107 and 104 | 11128 |
| 132 and 163 | 21516 |
| 10 and 120 | 120 |
| 15 and 103 | 1545 |