Least Common Multiple (LCM) of 96 and 71
The least common multiple (LCM) of 96 and 71 is 6816.
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 96 and 71?
First, calculate the GCD of 96 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 71 = 1 remainder 25 |
| 2 | 71 ÷ 25 = 2 remainder 21 |
| 3 | 25 ÷ 21 = 1 remainder 4 |
| 4 | 21 ÷ 4 = 5 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 160 | 640 |
| 118 and 126 | 7434 |
| 200 and 68 | 3400 |
| 53 and 49 | 2597 |
| 67 and 67 | 67 |