Least Common Multiple (LCM) of 112 and 190
The least common multiple (LCM) of 112 and 190 is 10640.
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 190?
First, calculate the GCD of 112 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 190 = 0 remainder 112 |
| 2 | 190 ÷ 112 = 1 remainder 78 |
| 3 | 112 ÷ 78 = 1 remainder 34 |
| 4 | 78 ÷ 34 = 2 remainder 10 |
| 5 | 34 ÷ 10 = 3 remainder 4 |
| 6 | 10 ÷ 4 = 2 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 182 | 34034 |
| 18 and 23 | 414 |
| 109 and 154 | 16786 |
| 192 and 175 | 33600 |
| 40 and 141 | 5640 |