Least Common Multiple (LCM) of 104 and 65
The least common multiple (LCM) of 104 and 65 is 520.
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 104 and 65?
First, calculate the GCD of 104 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 65 = 1 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 |
|---|---|
| 128 and 36 | 1152 |
| 147 and 90 | 4410 |
| 108 and 196 | 5292 |
| 65 and 22 | 1430 |
| 186 and 48 | 1488 |