Least Common Multiple (LCM) of 65 and 25
The least common multiple (LCM) of 65 and 25 is 325.
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 25?
First, calculate the GCD of 65 and 25 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 25 = 2 remainder 15 |
| 2 | 25 ÷ 15 = 1 remainder 10 |
| 3 | 15 ÷ 10 = 1 remainder 5 |
| 4 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 48 | 8400 |
| 84 and 25 | 2100 |
| 67 and 131 | 8777 |
| 130 and 170 | 2210 |
| 97 and 59 | 5723 |