Least Common Multiple (LCM) of 109 and 130
The least common multiple (LCM) of 109 and 130 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 109 and 130?
First, calculate the GCD of 109 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 130 = 0 remainder 109 |
| 2 | 130 ÷ 109 = 1 remainder 21 |
| 3 | 109 ÷ 21 = 5 remainder 4 |
| 4 | 21 ÷ 4 = 5 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 89 | 15130 |
| 198 and 165 | 990 |
| 39 and 56 | 2184 |
| 55 and 45 | 495 |
| 152 and 132 | 5016 |