Least Common Multiple (LCM) of 114 and 83
The least common multiple (LCM) of 114 and 83 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 114 and 83?
First, calculate the GCD of 114 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 83 = 1 remainder 31 |
| 2 | 83 ÷ 31 = 2 remainder 21 |
| 3 | 31 ÷ 21 = 1 remainder 10 |
| 4 | 21 ÷ 10 = 2 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 106 | 17066 |
| 49 and 138 | 6762 |
| 31 and 66 | 2046 |
| 68 and 171 | 11628 |
| 73 and 57 | 4161 |