Least Common Multiple (LCM) of 39 and 65
The least common multiple (LCM) of 39 and 65 is 195.
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 65?
First, calculate the GCD of 39 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 39 ÷ 65 = 0 remainder 39 |
| 2 | 65 ÷ 39 = 1 remainder 26 |
| 3 | 39 ÷ 26 = 1 remainder 13 |
| 4 | 26 ÷ 13 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 138 | 10074 |
| 198 and 144 | 1584 |
| 44 and 181 | 7964 |
| 115 and 157 | 18055 |
| 188 and 59 | 11092 |