Least Common Multiple (LCM) of 25 and 65
The least common multiple (LCM) of 25 and 65 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 25 and 65?
First, calculate the GCD of 25 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 25 ÷ 65 = 0 remainder 25 |
| 2 | 65 ÷ 25 = 2 remainder 15 |
| 3 | 25 ÷ 15 = 1 remainder 10 |
| 4 | 15 ÷ 10 = 1 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 66 | 4884 |
| 189 and 94 | 17766 |
| 130 and 154 | 10010 |
| 132 and 153 | 6732 |
| 136 and 77 | 10472 |