Least Common Multiple (LCM) of 199 and 23
The least common multiple (LCM) of 199 and 23 is 4577.
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 23?
First, calculate the GCD of 199 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 23 = 8 remainder 15 |
| 2 | 23 ÷ 15 = 1 remainder 8 |
| 3 | 15 ÷ 8 = 1 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 154 | 10626 |
| 17 and 127 | 2159 |
| 144 and 29 | 4176 |
| 14 and 114 | 798 |
| 90 and 75 | 450 |