Least Common Multiple (LCM) of 65 and 127
The least common multiple (LCM) of 65 and 127 is 8255.
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 127?
First, calculate the GCD of 65 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 127 = 0 remainder 65 |
| 2 | 127 ÷ 65 = 1 remainder 62 |
| 3 | 65 ÷ 62 = 1 remainder 3 |
| 4 | 62 ÷ 3 = 20 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 35 | 1855 |
| 164 and 113 | 18532 |
| 41 and 70 | 2870 |
| 135 and 55 | 1485 |
| 23 and 97 | 2231 |