Least Common Multiple (LCM) of 49 and 130
The least common multiple (LCM) of 49 and 130 is 6370.
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 49 and 130?
First, calculate the GCD of 49 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 130 = 0 remainder 49 |
| 2 | 130 ÷ 49 = 2 remainder 32 |
| 3 | 49 ÷ 32 = 1 remainder 17 |
| 4 | 32 ÷ 17 = 1 remainder 15 |
| 5 | 17 ÷ 15 = 1 remainder 2 |
| 6 | 15 ÷ 2 = 7 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 130 | 260 |
| 75 and 171 | 4275 |
| 85 and 91 | 7735 |
| 125 and 169 | 21125 |
| 138 and 22 | 1518 |