Least Common Multiple (LCM) of 130 and 106
The least common multiple (LCM) of 130 and 106 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 130 and 106?
First, calculate the GCD of 130 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 106 = 1 remainder 24 |
| 2 | 106 ÷ 24 = 4 remainder 10 |
| 3 | 24 ÷ 10 = 2 remainder 4 |
| 4 | 10 ÷ 4 = 2 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 110 | 10780 |
| 98 and 98 | 98 |
| 24 and 50 | 600 |
| 143 and 85 | 12155 |
| 110 and 31 | 3410 |