Least Common Multiple (LCM) of 112 and 199
The least common multiple (LCM) of 112 and 199 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 112 and 199?
First, calculate the GCD of 112 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 199 = 0 remainder 112 |
| 2 | 199 ÷ 112 = 1 remainder 87 |
| 3 | 112 ÷ 87 = 1 remainder 25 |
| 4 | 87 ÷ 25 = 3 remainder 12 |
| 5 | 25 ÷ 12 = 2 remainder 1 |
| 6 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 54 | 1728 |
| 45 and 183 | 2745 |
| 190 and 74 | 7030 |
| 78 and 46 | 1794 |
| 132 and 152 | 5016 |