Least Common Multiple (LCM) of 115 and 130
The least common multiple (LCM) of 115 and 130 is 2990.
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 115 and 130?
First, calculate the GCD of 115 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 130 = 0 remainder 115 |
| 2 | 130 ÷ 115 = 1 remainder 15 |
| 3 | 115 ÷ 15 = 7 remainder 10 |
| 4 | 15 ÷ 10 = 1 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 71 | 9230 |
| 131 and 82 | 10742 |
| 160 and 31 | 4960 |
| 135 and 68 | 9180 |
| 54 and 19 | 1026 |