Least Common Multiple (LCM) of 180 and 128
The least common multiple (LCM) of 180 and 128 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 180 and 128?
First, calculate the GCD of 180 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 128 = 1 remainder 52 |
| 2 | 128 ÷ 52 = 2 remainder 24 |
| 3 | 52 ÷ 24 = 2 remainder 4 |
| 4 | 24 ÷ 4 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 31 | 992 |
| 77 and 180 | 13860 |
| 155 and 37 | 5735 |
| 36 and 42 | 252 |
| 59 and 87 | 5133 |