Least Common Multiple (LCM) of 102 and 193
The least common multiple (LCM) of 102 and 193 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 102 and 193?
First, calculate the GCD of 102 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 193 = 0 remainder 102 |
| 2 | 193 ÷ 102 = 1 remainder 91 |
| 3 | 102 ÷ 91 = 1 remainder 11 |
| 4 | 91 ÷ 11 = 8 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 91 | 16380 |
| 31 and 24 | 744 |
| 161 and 193 | 31073 |
| 16 and 69 | 1104 |
| 24 and 105 | 840 |