Least Common Multiple (LCM) of 199 and 90
The least common multiple (LCM) of 199 and 90 is 17910.
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 90?
First, calculate the GCD of 199 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 90 = 2 remainder 19 |
| 2 | 90 ÷ 19 = 4 remainder 14 |
| 3 | 19 ÷ 14 = 1 remainder 5 |
| 4 | 14 ÷ 5 = 2 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 131 | 23580 |
| 142 and 141 | 20022 |
| 177 and 198 | 11682 |
| 32 and 181 | 5792 |
| 132 and 156 | 1716 |