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 |
|---|---|
| 165 and 148 | 24420 |
| 129 and 53 | 6837 |
| 35 and 174 | 6090 |
| 102 and 79 | 8058 |
| 174 and 104 | 9048 |