Least Common Multiple (LCM) of 193 and 104
The least common multiple (LCM) of 193 and 104 is 20072.
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 104?
First, calculate the GCD of 193 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 104 = 1 remainder 89 |
| 2 | 104 ÷ 89 = 1 remainder 15 |
| 3 | 89 ÷ 15 = 5 remainder 14 |
| 4 | 15 ÷ 14 = 1 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 35 | 5985 |
| 186 and 169 | 31434 |
| 156 and 19 | 2964 |
| 100 and 184 | 4600 |
| 76 and 23 | 1748 |