Least Common Multiple (LCM) of 112 and 193
The least common multiple (LCM) of 112 and 193 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 112 and 193?
First, calculate the GCD of 112 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 193 = 0 remainder 112 |
| 2 | 193 ÷ 112 = 1 remainder 81 |
| 3 | 112 ÷ 81 = 1 remainder 31 |
| 4 | 81 ÷ 31 = 2 remainder 19 |
| 5 | 31 ÷ 19 = 1 remainder 12 |
| 6 | 19 ÷ 12 = 1 remainder 7 |
| 7 | 12 ÷ 7 = 1 remainder 5 |
| 8 | 7 ÷ 5 = 1 remainder 2 |
| 9 | 5 ÷ 2 = 2 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 162 | 5184 |
| 86 and 157 | 13502 |
| 50 and 172 | 4300 |
| 137 and 58 | 7946 |
| 166 and 75 | 12450 |