Least Common Multiple (LCM) of 45 and 32
The least common multiple (LCM) of 45 and 32 is 1440.
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 32?
First, calculate the GCD of 45 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 32 = 1 remainder 13 |
| 2 | 32 ÷ 13 = 2 remainder 6 |
| 3 | 13 ÷ 6 = 2 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 19 | 304 |
| 117 and 33 | 1287 |
| 71 and 13 | 923 |
| 59 and 47 | 2773 |
| 112 and 28 | 112 |