Least Common Multiple (LCM) of 71 and 128
The least common multiple (LCM) of 71 and 128 is 9088.
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 71 and 128?
First, calculate the GCD of 71 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 128 = 0 remainder 71 |
| 2 | 128 ÷ 71 = 1 remainder 57 |
| 3 | 71 ÷ 57 = 1 remainder 14 |
| 4 | 57 ÷ 14 = 4 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 15 | 345 |
| 133 and 161 | 3059 |
| 145 and 83 | 12035 |
| 13 and 175 | 2275 |
| 131 and 113 | 14803 |