Least Common Multiple (LCM) of 50 and 130
The least common multiple (LCM) of 50 and 130 is 650.
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 50 and 130?
First, calculate the GCD of 50 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 130 = 0 remainder 50 |
| 2 | 130 ÷ 50 = 2 remainder 30 |
| 3 | 50 ÷ 30 = 1 remainder 20 |
| 4 | 30 ÷ 20 = 1 remainder 10 |
| 5 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 26 | 2678 |
| 56 and 130 | 3640 |
| 96 and 200 | 2400 |
| 178 and 105 | 18690 |
| 10 and 155 | 310 |