Least Common Multiple (LCM) of 193 and 84
The least common multiple (LCM) of 193 and 84 is 16212.
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 84?
First, calculate the GCD of 193 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 84 = 2 remainder 25 |
| 2 | 84 ÷ 25 = 3 remainder 9 |
| 3 | 25 ÷ 9 = 2 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 169 | 6760 |
| 62 and 95 | 5890 |
| 104 and 75 | 7800 |
| 144 and 90 | 720 |
| 124 and 81 | 10044 |