Least Common Multiple (LCM) of 106 and 130
The least common multiple (LCM) of 106 and 130 is 6890.
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 106 and 130?
First, calculate the GCD of 106 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 130 = 0 remainder 106 |
| 2 | 130 ÷ 106 = 1 remainder 24 |
| 3 | 106 ÷ 24 = 4 remainder 10 |
| 4 | 24 ÷ 10 = 2 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 188 | 14476 |
| 106 and 196 | 10388 |
| 46 and 137 | 6302 |
| 118 and 147 | 17346 |
| 80 and 10 | 80 |