Least Common Multiple (LCM) of 83 and 194
The least common multiple (LCM) of 83 and 194 is 16102.
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 194?
First, calculate the GCD of 83 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 194 = 0 remainder 83 |
| 2 | 194 ÷ 83 = 2 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 |
|---|---|
| 141 and 92 | 12972 |
| 98 and 113 | 11074 |
| 35 and 23 | 805 |
| 135 and 164 | 22140 |
| 63 and 47 | 2961 |