Least Common Multiple (LCM) of 130 and 81
The least common multiple (LCM) of 130 and 81 is 10530.
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 81?
First, calculate the GCD of 130 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 81 = 1 remainder 49 |
| 2 | 81 ÷ 49 = 1 remainder 32 |
| 3 | 49 ÷ 32 = 1 remainder 17 |
| 4 | 32 ÷ 17 = 1 remainder 15 |
| 5 | 17 ÷ 15 = 1 remainder 2 |
| 6 | 15 ÷ 2 = 7 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 129 | 18705 |
| 21 and 142 | 2982 |
| 107 and 143 | 15301 |
| 141 and 140 | 19740 |
| 192 and 180 | 2880 |