Least Common Multiple (LCM) of 45 and 128
The least common multiple (LCM) of 45 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 45 and 128?
First, calculate the GCD of 45 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 128 = 0 remainder 45 |
| 2 | 128 ÷ 45 = 2 remainder 38 |
| 3 | 45 ÷ 38 = 1 remainder 7 |
| 4 | 38 ÷ 7 = 5 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 164 | 820 |
| 43 and 15 | 645 |
| 181 and 37 | 6697 |
| 25 and 132 | 3300 |
| 184 and 197 | 36248 |