Least Common Multiple (LCM) of 80 and 128
The least common multiple (LCM) of 80 and 128 is 640.
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 128?
First, calculate the GCD of 80 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 128 = 0 remainder 80 |
| 2 | 128 ÷ 80 = 1 remainder 48 |
| 3 | 80 ÷ 48 = 1 remainder 32 |
| 4 | 48 ÷ 32 = 1 remainder 16 |
| 5 | 32 ÷ 16 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 141 | 8460 |
| 136 and 105 | 14280 |
| 23 and 111 | 2553 |
| 88 and 130 | 5720 |
| 107 and 50 | 5350 |