Least Common Multiple (LCM) of 130 and 97
The least common multiple (LCM) of 130 and 97 is 12610.
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 97?
First, calculate the GCD of 130 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 97 = 1 remainder 33 |
| 2 | 97 ÷ 33 = 2 remainder 31 |
| 3 | 33 ÷ 31 = 1 remainder 2 |
| 4 | 31 ÷ 2 = 15 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 71 | 5467 |
| 38 and 177 | 6726 |
| 17 and 169 | 2873 |
| 75 and 165 | 825 |
| 152 and 175 | 26600 |