Least Common Multiple (LCM) of 65 and 41
The least common multiple (LCM) of 65 and 41 is 2665.
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 65 and 41?
First, calculate the GCD of 65 and 41 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 41 = 1 remainder 24 |
| 2 | 41 ÷ 24 = 1 remainder 17 |
| 3 | 24 ÷ 17 = 1 remainder 7 |
| 4 | 17 ÷ 7 = 2 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 146 | 4964 |
| 167 and 141 | 23547 |
| 88 and 104 | 1144 |
| 41 and 192 | 7872 |
| 185 and 124 | 22940 |