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 |
|---|---|
| 51 and 150 | 2550 |
| 188 and 82 | 7708 |
| 59 and 50 | 2950 |
| 69 and 40 | 2760 |
| 139 and 25 | 3475 |