Least Common Multiple (LCM) of 71 and 96
The least common multiple (LCM) of 71 and 96 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 71 and 96?
First, calculate the GCD of 71 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 96 = 0 remainder 71 |
| 2 | 96 ÷ 71 = 1 remainder 25 |
| 3 | 71 ÷ 25 = 2 remainder 21 |
| 4 | 25 ÷ 21 = 1 remainder 4 |
| 5 | 21 ÷ 4 = 5 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 79 | 2370 |
| 136 and 56 | 952 |
| 138 and 87 | 4002 |
| 176 and 61 | 10736 |
| 199 and 45 | 8955 |