Least Common Multiple (LCM) of 65 and 73
The least common multiple (LCM) of 65 and 73 is 4745.
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 73?
First, calculate the GCD of 65 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 73 = 0 remainder 65 |
| 2 | 73 ÷ 65 = 1 remainder 8 |
| 3 | 65 ÷ 8 = 8 remainder 1 |
| 4 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 138 | 1518 |
| 152 and 140 | 5320 |
| 152 and 105 | 15960 |
| 58 and 180 | 5220 |
| 196 and 78 | 7644 |