Least Common Multiple (LCM) of 83 and 131
The least common multiple (LCM) of 83 and 131 is 10873.
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 131?
First, calculate the GCD of 83 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 131 = 0 remainder 83 |
| 2 | 131 ÷ 83 = 1 remainder 48 |
| 3 | 83 ÷ 48 = 1 remainder 35 |
| 4 | 48 ÷ 35 = 1 remainder 13 |
| 5 | 35 ÷ 13 = 2 remainder 9 |
| 6 | 13 ÷ 9 = 1 remainder 4 |
| 7 | 9 ÷ 4 = 2 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 44 | 2244 |
| 108 and 37 | 3996 |
| 188 and 144 | 6768 |
| 98 and 132 | 6468 |
| 30 and 146 | 2190 |