Least Common Multiple (LCM) of 83 and 111
The least common multiple (LCM) of 83 and 111 is 9213.
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 111?
First, calculate the GCD of 83 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 111 = 0 remainder 83 |
| 2 | 111 ÷ 83 = 1 remainder 28 |
| 3 | 83 ÷ 28 = 2 remainder 27 |
| 4 | 28 ÷ 27 = 1 remainder 1 |
| 5 | 27 ÷ 1 = 27 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 178 | 20826 |
| 61 and 65 | 3965 |
| 171 and 103 | 17613 |
| 31 and 98 | 3038 |
| 143 and 43 | 6149 |