Least Common Multiple (LCM) of 75 and 130
The least common multiple (LCM) of 75 and 130 is 1950.
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 75 and 130?
First, calculate the GCD of 75 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 130 = 0 remainder 75 |
| 2 | 130 ÷ 75 = 1 remainder 55 |
| 3 | 75 ÷ 55 = 1 remainder 20 |
| 4 | 55 ÷ 20 = 2 remainder 15 |
| 5 | 20 ÷ 15 = 1 remainder 5 |
| 6 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 26 | 3874 |
| 17 and 16 | 272 |
| 125 and 77 | 9625 |
| 17 and 16 | 272 |
| 139 and 146 | 20294 |