Least Common Multiple (LCM) of 123 and 128
The least common multiple (LCM) of 123 and 128 is 15744.
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 128?
First, calculate the GCD of 123 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 128 = 0 remainder 123 |
| 2 | 128 ÷ 123 = 1 remainder 5 |
| 3 | 123 ÷ 5 = 24 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 45 | 180 |
| 109 and 158 | 17222 |
| 112 and 81 | 9072 |
| 119 and 167 | 19873 |
| 84 and 77 | 924 |