Least Common Multiple (LCM) of 83 and 114
The least common multiple (LCM) of 83 and 114 is 9462.
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 114?
First, calculate the GCD of 83 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 114 = 0 remainder 83 |
| 2 | 114 ÷ 83 = 1 remainder 31 |
| 3 | 83 ÷ 31 = 2 remainder 21 |
| 4 | 31 ÷ 21 = 1 remainder 10 |
| 5 | 21 ÷ 10 = 2 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 117 | 2340 |
| 80 and 122 | 4880 |
| 41 and 68 | 2788 |
| 62 and 194 | 6014 |
| 181 and 111 | 20091 |