Least Common Multiple (LCM) of 123 and 56
The least common multiple (LCM) of 123 and 56 is 6888.
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 56?
First, calculate the GCD of 123 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 56 = 2 remainder 11 |
| 2 | 56 ÷ 11 = 5 remainder 1 |
| 3 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 35 | 945 |
| 77 and 137 | 10549 |
| 137 and 146 | 20002 |
| 80 and 19 | 1520 |
| 190 and 173 | 32870 |