Least Common Multiple (LCM) of 112 and 194
The least common multiple (LCM) of 112 and 194 is 10864.
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 194?
First, calculate the GCD of 112 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 194 = 0 remainder 112 |
| 2 | 194 ÷ 112 = 1 remainder 82 |
| 3 | 112 ÷ 82 = 1 remainder 30 |
| 4 | 82 ÷ 30 = 2 remainder 22 |
| 5 | 30 ÷ 22 = 1 remainder 8 |
| 6 | 22 ÷ 8 = 2 remainder 6 |
| 7 | 8 ÷ 6 = 1 remainder 2 |
| 8 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 40 | 840 |
| 110 and 14 | 770 |
| 39 and 132 | 1716 |
| 113 and 164 | 18532 |
| 191 and 135 | 25785 |