Least Common Multiple (LCM) of 108 and 71
The least common multiple (LCM) of 108 and 71 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 108 and 71?
First, calculate the GCD of 108 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 71 = 1 remainder 37 |
| 2 | 71 ÷ 37 = 1 remainder 34 |
| 3 | 37 ÷ 34 = 1 remainder 3 |
| 4 | 34 ÷ 3 = 11 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 82 | 8446 |
| 69 and 144 | 3312 |
| 47 and 104 | 4888 |
| 33 and 17 | 561 |
| 130 and 61 | 7930 |