Least Common Multiple (LCM) of 65 and 163
The least common multiple (LCM) of 65 and 163 is 10595.
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 163?
First, calculate the GCD of 65 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 163 = 0 remainder 65 |
| 2 | 163 ÷ 65 = 2 remainder 33 |
| 3 | 65 ÷ 33 = 1 remainder 32 |
| 4 | 33 ÷ 32 = 1 remainder 1 |
| 5 | 32 ÷ 1 = 32 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 48 | 1200 |
| 186 and 103 | 19158 |
| 29 and 81 | 2349 |
| 191 and 69 | 13179 |
| 58 and 89 | 5162 |