Least Common Multiple (LCM) of 128 and 123
The least common multiple (LCM) of 128 and 123 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 128 and 123?
First, calculate the GCD of 128 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 123 = 1 remainder 5 |
| 2 | 123 ÷ 5 = 24 remainder 3 |
| 3 | 5 ÷ 3 = 1 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 154 | 2310 |
| 53 and 17 | 901 |
| 188 and 178 | 16732 |
| 121 and 40 | 4840 |
| 90 and 133 | 11970 |