Least Common Multiple (LCM) of 130 and 107
The least common multiple (LCM) of 130 and 107 is 13910.
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 107?
First, calculate the GCD of 130 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 107 = 1 remainder 23 |
| 2 | 107 ÷ 23 = 4 remainder 15 |
| 3 | 23 ÷ 15 = 1 remainder 8 |
| 4 | 15 ÷ 8 = 1 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 31 | 465 |
| 56 and 113 | 6328 |
| 39 and 80 | 3120 |
| 194 and 199 | 38606 |
| 169 and 74 | 12506 |