Least Common Multiple (LCM) of 105 and 130
The least common multiple (LCM) of 105 and 130 is 2730.
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 105 and 130?
First, calculate the GCD of 105 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 130 = 0 remainder 105 |
| 2 | 130 ÷ 105 = 1 remainder 25 |
| 3 | 105 ÷ 25 = 4 remainder 5 |
| 4 | 25 ÷ 5 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 106 | 2120 |
| 11 and 10 | 110 |
| 72 and 187 | 13464 |
| 173 and 156 | 26988 |
| 152 and 135 | 20520 |