Least Common Multiple (LCM) of 130 and 109
The least common multiple (LCM) of 130 and 109 is 14170.
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 109?
First, calculate the GCD of 130 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 109 = 1 remainder 21 |
| 2 | 109 ÷ 21 = 5 remainder 4 |
| 3 | 21 ÷ 4 = 5 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 114 | 4674 |
| 136 and 84 | 2856 |
| 60 and 64 | 960 |
| 12 and 130 | 780 |
| 77 and 91 | 1001 |