Least Common Multiple (LCM) of 39 and 109
The least common multiple (LCM) of 39 and 109 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 39 and 109?
First, calculate the GCD of 39 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 39 ÷ 109 = 0 remainder 39 |
| 2 | 109 ÷ 39 = 2 remainder 31 |
| 3 | 39 ÷ 31 = 1 remainder 8 |
| 4 | 31 ÷ 8 = 3 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 89 | 10235 |
| 87 and 170 | 14790 |
| 13 and 169 | 169 |
| 12 and 111 | 444 |
| 164 and 33 | 5412 |