Least Common Multiple (LCM) of 65 and 60
The least common multiple (LCM) of 65 and 60 is 780.
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 60?
First, calculate the GCD of 65 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 60 = 1 remainder 5 |
| 2 | 60 ÷ 5 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 72 | 4680 |
| 162 and 120 | 3240 |
| 180 and 193 | 34740 |
| 197 and 75 | 14775 |
| 189 and 153 | 3213 |