Least Common Multiple (LCM) of 65 and 69
The least common multiple (LCM) of 65 and 69 is 4485.
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 69?
First, calculate the GCD of 65 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 69 = 0 remainder 65 |
| 2 | 69 ÷ 65 = 1 remainder 4 |
| 3 | 65 ÷ 4 = 16 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 121 | 16093 |
| 85 and 111 | 9435 |
| 167 and 24 | 4008 |
| 150 and 180 | 900 |
| 147 and 185 | 27195 |