Least Common Multiple (LCM) of 199 and 176
The least common multiple (LCM) of 199 and 176 is 35024.
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 176?
First, calculate the GCD of 199 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 176 = 1 remainder 23 |
| 2 | 176 ÷ 23 = 7 remainder 15 |
| 3 | 23 ÷ 15 = 1 remainder 8 |
| 4 | 15 ÷ 8 = 1 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 31 | 434 |
| 72 and 185 | 13320 |
| 104 and 125 | 13000 |
| 135 and 57 | 2565 |
| 90 and 20 | 180 |