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 |
|---|---|
| 23 and 115 | 115 |
| 107 and 152 | 16264 |
| 170 and 94 | 7990 |
| 175 and 108 | 18900 |
| 29 and 68 | 1972 |