Least Common Multiple (LCM) of 23 and 128
The least common multiple (LCM) of 23 and 128 is 2944.
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 23 and 128?
First, calculate the GCD of 23 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 128 = 0 remainder 23 |
| 2 | 128 ÷ 23 = 5 remainder 13 |
| 3 | 23 ÷ 13 = 1 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 144 | 720 |
| 119 and 140 | 2380 |
| 171 and 161 | 27531 |
| 64 and 158 | 5056 |
| 19 and 138 | 2622 |