Least Common Multiple (LCM) of 123 and 112
The least common multiple (LCM) of 123 and 112 is 13776.
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 123 and 112?
First, calculate the GCD of 123 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 112 = 1 remainder 11 |
| 2 | 112 ÷ 11 = 10 remainder 2 |
| 3 | 11 ÷ 2 = 5 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 95 | 5795 |
| 18 and 24 | 72 |
| 89 and 66 | 5874 |
| 23 and 13 | 299 |
| 186 and 188 | 17484 |