Least Common Multiple (LCM) of 108 and 39
The least common multiple (LCM) of 108 and 39 is 1404.
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 39?
First, calculate the GCD of 108 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 39 = 2 remainder 30 |
| 2 | 39 ÷ 30 = 1 remainder 9 |
| 3 | 30 ÷ 9 = 3 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 68 | 1700 |
| 35 and 188 | 6580 |
| 187 and 104 | 19448 |
| 84 and 90 | 1260 |
| 113 and 16 | 1808 |