Least Common Multiple (LCM) of 83 and 12
The least common multiple (LCM) of 83 and 12 is 996.
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 12?
First, calculate the GCD of 83 and 12 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 12 = 6 remainder 11 |
| 2 | 12 ÷ 11 = 1 remainder 1 |
| 3 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 140 | 11340 |
| 42 and 104 | 2184 |
| 147 and 102 | 4998 |
| 159 and 109 | 17331 |
| 122 and 134 | 8174 |