Least Common Multiple (LCM) of 128 and 45
The least common multiple (LCM) of 128 and 45 is 5760.
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 128 and 45?
First, calculate the GCD of 128 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 45 = 2 remainder 38 |
| 2 | 45 ÷ 38 = 1 remainder 7 |
| 3 | 38 ÷ 7 = 5 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 155 | 16120 |
| 72 and 57 | 1368 |
| 12 and 121 | 1452 |
| 128 and 31 | 3968 |
| 23 and 30 | 690 |