Least Common Multiple (LCM) of 112 and 45
The least common multiple (LCM) of 112 and 45 is 5040.
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 112 and 45?
First, calculate the GCD of 112 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 45 = 2 remainder 22 |
| 2 | 45 ÷ 22 = 2 remainder 1 |
| 3 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 120 | 3960 |
| 15 and 185 | 555 |
| 142 and 42 | 2982 |
| 13 and 158 | 2054 |
| 14 and 171 | 2394 |