Least Common Multiple (LCM) of 130 and 196
The least common multiple (LCM) of 130 and 196 is 12740.
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 196?
First, calculate the GCD of 130 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 196 = 0 remainder 130 |
| 2 | 196 ÷ 130 = 1 remainder 66 |
| 3 | 130 ÷ 66 = 1 remainder 64 |
| 4 | 66 ÷ 64 = 1 remainder 2 |
| 5 | 64 ÷ 2 = 32 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 120 | 600 |
| 101 and 150 | 15150 |
| 174 and 41 | 7134 |
| 142 and 192 | 13632 |
| 55 and 179 | 9845 |