Least Common Multiple (LCM) of 71 and 108
The least common multiple (LCM) of 71 and 108 is 7668.
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 108?
First, calculate the GCD of 71 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 108 = 0 remainder 71 |
| 2 | 108 ÷ 71 = 1 remainder 37 |
| 3 | 71 ÷ 37 = 1 remainder 34 |
| 4 | 37 ÷ 34 = 1 remainder 3 |
| 5 | 34 ÷ 3 = 11 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 188 | 4700 |
| 137 and 37 | 5069 |
| 135 and 79 | 10665 |
| 81 and 26 | 2106 |
| 21 and 125 | 2625 |