Least Common Multiple (LCM) of 65 and 128
The least common multiple (LCM) of 65 and 128 is 8320.
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 128?
First, calculate the GCD of 65 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 128 = 0 remainder 65 |
| 2 | 128 ÷ 65 = 1 remainder 63 |
| 3 | 65 ÷ 63 = 1 remainder 2 |
| 4 | 63 ÷ 2 = 31 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 198 | 13266 |
| 60 and 111 | 2220 |
| 47 and 105 | 4935 |
| 149 and 103 | 15347 |
| 57 and 119 | 6783 |