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 |
|---|---|
| 113 and 28 | 3164 |
| 16 and 35 | 560 |
| 126 and 17 | 2142 |
| 49 and 168 | 1176 |
| 22 and 45 | 990 |