Least Common Multiple (LCM) of 130 and 75
The least common multiple (LCM) of 130 and 75 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 130 and 75?
First, calculate the GCD of 130 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 75 = 1 remainder 55 |
| 2 | 75 ÷ 55 = 1 remainder 20 |
| 3 | 55 ÷ 20 = 2 remainder 15 |
| 4 | 20 ÷ 15 = 1 remainder 5 |
| 5 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 94 | 3760 |
| 77 and 57 | 4389 |
| 142 and 39 | 5538 |
| 110 and 161 | 17710 |
| 199 and 67 | 13333 |