Least Common Multiple (LCM) of 83 and 130
The least common multiple (LCM) of 83 and 130 is 10790.
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 83 and 130?
First, calculate the GCD of 83 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 130 = 0 remainder 83 |
| 2 | 130 ÷ 83 = 1 remainder 47 |
| 3 | 83 ÷ 47 = 1 remainder 36 |
| 4 | 47 ÷ 36 = 1 remainder 11 |
| 5 | 36 ÷ 11 = 3 remainder 3 |
| 6 | 11 ÷ 3 = 3 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 105 | 1995 |
| 23 and 104 | 2392 |
| 145 and 87 | 435 |
| 181 and 72 | 13032 |
| 198 and 146 | 14454 |