Least Common Multiple (LCM) of 54 and 80
The least common multiple (LCM) of 54 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 54 and 80?
First, calculate the GCD of 54 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 80 = 0 remainder 54 |
| 2 | 80 ÷ 54 = 1 remainder 26 |
| 3 | 54 ÷ 26 = 2 remainder 2 |
| 4 | 26 ÷ 2 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 126 | 15246 |
| 110 and 162 | 8910 |
| 120 and 109 | 13080 |
| 178 and 182 | 16198 |
| 129 and 127 | 16383 |