Least Common Multiple (LCM) of 21 and 199
The least common multiple (LCM) of 21 and 199 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 21 and 199?
First, calculate the GCD of 21 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 199 = 0 remainder 21 |
| 2 | 199 ÷ 21 = 9 remainder 10 |
| 3 | 21 ÷ 10 = 2 remainder 1 |
| 4 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 79 | 13667 |
| 15 and 194 | 2910 |
| 133 and 159 | 21147 |
| 72 and 134 | 4824 |
| 48 and 117 | 1872 |