Least Common Multiple (LCM) of 15 and 128
The least common multiple (LCM) of 15 and 128 is 1920.
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 15 and 128?
First, calculate the GCD of 15 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 15 ÷ 128 = 0 remainder 15 |
| 2 | 128 ÷ 15 = 8 remainder 8 |
| 3 | 15 ÷ 8 = 1 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 112 | 1680 |
| 199 and 14 | 2786 |
| 53 and 59 | 3127 |
| 163 and 117 | 19071 |
| 105 and 95 | 1995 |