Least Common Multiple (LCM) of 199 and 112
The least common multiple (LCM) of 199 and 112 is 22288.
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 199 and 112?
First, calculate the GCD of 199 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 112 = 1 remainder 87 |
| 2 | 112 ÷ 87 = 1 remainder 25 |
| 3 | 87 ÷ 25 = 3 remainder 12 |
| 4 | 25 ÷ 12 = 2 remainder 1 |
| 5 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 141 | 705 |
| 101 and 151 | 15251 |
| 131 and 135 | 17685 |
| 103 and 163 | 16789 |
| 18 and 20 | 180 |