Least Common Multiple (LCM) of 45 and 199
The least common multiple (LCM) of 45 and 199 is 8955.
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 45 and 199?
First, calculate the GCD of 45 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 199 = 0 remainder 45 |
| 2 | 199 ÷ 45 = 4 remainder 19 |
| 3 | 45 ÷ 19 = 2 remainder 7 |
| 4 | 19 ÷ 7 = 2 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 159 | 9540 |
| 93 and 69 | 2139 |
| 50 and 188 | 4700 |
| 146 and 22 | 1606 |
| 55 and 181 | 9955 |