Least Common Multiple (LCM) of 130 and 200
The least common multiple (LCM) of 130 and 200 is 2600.
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 200?
First, calculate the GCD of 130 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 200 = 0 remainder 130 |
| 2 | 200 ÷ 130 = 1 remainder 70 |
| 3 | 130 ÷ 70 = 1 remainder 60 |
| 4 | 70 ÷ 60 = 1 remainder 10 |
| 5 | 60 ÷ 10 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 44 and 32 | 352 |
| 130 and 149 | 19370 |
| 113 and 120 | 13560 |
| 144 and 163 | 23472 |
| 112 and 83 | 9296 |