Least Common Multiple (LCM) of 81 and 130
The least common multiple (LCM) of 81 and 130 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 81 and 130?
First, calculate the GCD of 81 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 130 = 0 remainder 81 |
| 2 | 130 ÷ 81 = 1 remainder 49 |
| 3 | 81 ÷ 49 = 1 remainder 32 |
| 4 | 49 ÷ 32 = 1 remainder 17 |
| 5 | 32 ÷ 17 = 1 remainder 15 |
| 6 | 17 ÷ 15 = 1 remainder 2 |
| 7 | 15 ÷ 2 = 7 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 164 | 9020 |
| 111 and 181 | 20091 |
| 77 and 59 | 4543 |
| 75 and 30 | 150 |
| 157 and 112 | 17584 |