Least Common Multiple (LCM) of 193 and 102
The least common multiple (LCM) of 193 and 102 is 19686.
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 193 and 102?
First, calculate the GCD of 193 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 102 = 1 remainder 91 |
| 2 | 102 ÷ 91 = 1 remainder 11 |
| 3 | 91 ÷ 11 = 8 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 104 | 104 |
| 72 and 81 | 648 |
| 112 and 134 | 7504 |
| 22 and 75 | 1650 |
| 103 and 27 | 2781 |