Least Common Multiple (LCM) of 193 and 112
The least common multiple (LCM) of 193 and 112 is 21616.
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 112?
First, calculate the GCD of 193 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 112 = 1 remainder 81 |
| 2 | 112 ÷ 81 = 1 remainder 31 |
| 3 | 81 ÷ 31 = 2 remainder 19 |
| 4 | 31 ÷ 19 = 1 remainder 12 |
| 5 | 19 ÷ 12 = 1 remainder 7 |
| 6 | 12 ÷ 7 = 1 remainder 5 |
| 7 | 7 ÷ 5 = 1 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 161 | 31878 |
| 173 and 191 | 33043 |
| 141 and 109 | 15369 |
| 192 and 68 | 3264 |
| 63 and 134 | 8442 |