Least Common Multiple (LCM) of 13 and 83
The least common multiple (LCM) of 13 and 83 is 1079.
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 13 and 83?
First, calculate the GCD of 13 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 83 = 0 remainder 13 |
| 2 | 83 ÷ 13 = 6 remainder 5 |
| 3 | 13 ÷ 5 = 2 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 105 | 11445 |
| 161 and 33 | 5313 |
| 135 and 64 | 8640 |
| 200 and 48 | 1200 |
| 106 and 84 | 4452 |