Least Common Multiple (LCM) of 199 and 180
The least common multiple (LCM) of 199 and 180 is 35820.
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 180?
First, calculate the GCD of 199 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 180 = 1 remainder 19 |
| 2 | 180 ÷ 19 = 9 remainder 9 |
| 3 | 19 ÷ 9 = 2 remainder 1 |
| 4 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 42 | 2226 |
| 47 and 125 | 5875 |
| 114 and 101 | 11514 |
| 48 and 76 | 912 |
| 60 and 85 | 1020 |