Least Common Multiple (LCM) of 112 and 123
The least common multiple (LCM) of 112 and 123 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 112 and 123?
First, calculate the GCD of 112 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 123 = 0 remainder 112 |
| 2 | 123 ÷ 112 = 1 remainder 11 |
| 3 | 112 ÷ 11 = 10 remainder 2 |
| 4 | 11 ÷ 2 = 5 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 145 | 21605 |
| 141 and 56 | 7896 |
| 168 and 42 | 168 |
| 175 and 163 | 28525 |
| 112 and 85 | 9520 |