Least Common Multiple (LCM) of 55 and 128
The least common multiple (LCM) of 55 and 128 is 7040.
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 55 and 128?
First, calculate the GCD of 55 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 128 = 0 remainder 55 |
| 2 | 128 ÷ 55 = 2 remainder 18 |
| 3 | 55 ÷ 18 = 3 remainder 1 |
| 4 | 18 ÷ 1 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 60 | 1140 |
| 76 and 125 | 9500 |
| 34 and 122 | 2074 |
| 75 and 84 | 2100 |
| 118 and 18 | 1062 |