Least Common Multiple (LCM) of 102 and 194
The least common multiple (LCM) of 102 and 194 is 9894.
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 102 and 194?
First, calculate the GCD of 102 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 194 = 0 remainder 102 |
| 2 | 194 ÷ 102 = 1 remainder 92 |
| 3 | 102 ÷ 92 = 1 remainder 10 |
| 4 | 92 ÷ 10 = 9 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 156 | 2964 |
| 22 and 200 | 2200 |
| 83 and 17 | 1411 |
| 94 and 74 | 3478 |
| 114 and 160 | 9120 |