Least Common Multiple (LCM) of 128 and 180
The least common multiple (LCM) of 128 and 180 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 180?
First, calculate the GCD of 128 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 180 = 0 remainder 128 |
| 2 | 180 ÷ 128 = 1 remainder 52 |
| 3 | 128 ÷ 52 = 2 remainder 24 |
| 4 | 52 ÷ 24 = 2 remainder 4 |
| 5 | 24 ÷ 4 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 53 | 530 |
| 45 and 77 | 3465 |
| 92 and 71 | 6532 |
| 59 and 38 | 2242 |
| 84 and 113 | 9492 |