Least Common Multiple (LCM) of 114 and 112
The least common multiple (LCM) of 114 and 112 is 6384.
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 114 and 112?
First, calculate the GCD of 114 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 112 = 1 remainder 2 |
| 2 | 112 ÷ 2 = 56 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 65 | 1365 |
| 21 and 62 | 1302 |
| 131 and 179 | 23449 |
| 82 and 196 | 8036 |
| 192 and 149 | 28608 |