Least Common Multiple (LCM) of 19 and 128
The least common multiple (LCM) of 19 and 128 is 2432.
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 19 and 128?
First, calculate the GCD of 19 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 128 = 0 remainder 19 |
| 2 | 128 ÷ 19 = 6 remainder 14 |
| 3 | 19 ÷ 14 = 1 remainder 5 |
| 4 | 14 ÷ 5 = 2 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 103 | 12051 |
| 180 and 176 | 7920 |
| 83 and 105 | 8715 |
| 27 and 127 | 3429 |
| 54 and 82 | 2214 |