Least Common Multiple (LCM) of 199 and 21
The least common multiple (LCM) of 199 and 21 is 4179.
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 21?
First, calculate the GCD of 199 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 21 = 9 remainder 10 |
| 2 | 21 ÷ 10 = 2 remainder 1 |
| 3 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 168 | 7224 |
| 17 and 133 | 2261 |
| 87 and 81 | 2349 |
| 58 and 111 | 6438 |
| 21 and 60 | 420 |