Least Common Multiple (LCM) of 108 and 130
The least common multiple (LCM) of 108 and 130 is 7020.
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 108 and 130?
First, calculate the GCD of 108 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 130 = 0 remainder 108 |
| 2 | 130 ÷ 108 = 1 remainder 22 |
| 3 | 108 ÷ 22 = 4 remainder 20 |
| 4 | 22 ÷ 20 = 1 remainder 2 |
| 5 | 20 ÷ 2 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 125 | 875 |
| 193 and 143 | 27599 |
| 90 and 116 | 5220 |
| 185 and 74 | 370 |
| 177 and 58 | 10266 |