Least Common Multiple (LCM) of 45 and 192
The least common multiple (LCM) of 45 and 192 is 2880.
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 192?
First, calculate the GCD of 45 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 192 = 0 remainder 45 |
| 2 | 192 ÷ 45 = 4 remainder 12 |
| 3 | 45 ÷ 12 = 3 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 164 | 25420 |
| 24 and 132 | 264 |
| 71 and 174 | 12354 |
| 196 and 59 | 11564 |
| 75 and 24 | 600 |