Least Common Multiple (LCM) of 120 and 128
The least common multiple (LCM) of 120 and 128 is 1920.
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 120 and 128?
First, calculate the GCD of 120 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 128 = 0 remainder 120 |
| 2 | 128 ÷ 120 = 1 remainder 8 |
| 3 | 120 ÷ 8 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 178 | 14418 |
| 105 and 132 | 4620 |
| 137 and 64 | 8768 |
| 130 and 153 | 19890 |
| 177 and 91 | 16107 |