Least Common Multiple (LCM) of 109 and 39
The least common multiple (LCM) of 109 and 39 is 4251.
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 109 and 39?
First, calculate the GCD of 109 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 39 = 2 remainder 31 |
| 2 | 39 ÷ 31 = 1 remainder 8 |
| 3 | 31 ÷ 8 = 3 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 143 | 15301 |
| 169 and 185 | 31265 |
| 66 and 159 | 3498 |
| 140 and 77 | 1540 |
| 135 and 48 | 2160 |