Least Common Multiple (LCM) of 65 and 125
The least common multiple (LCM) of 65 and 125 is 1625.
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 125?
First, calculate the GCD of 65 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 125 = 0 remainder 65 |
| 2 | 125 ÷ 65 = 1 remainder 60 |
| 3 | 65 ÷ 60 = 1 remainder 5 |
| 4 | 60 ÷ 5 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 128 | 11136 |
| 159 and 134 | 21306 |
| 171 and 88 | 15048 |
| 116 and 105 | 12180 |
| 86 and 78 | 3354 |