Least Common Multiple (LCM) of 23 and 199
The least common multiple (LCM) of 23 and 199 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 23 and 199?
First, calculate the GCD of 23 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 199 = 0 remainder 23 |
| 2 | 199 ÷ 23 = 8 remainder 15 |
| 3 | 23 ÷ 15 = 1 remainder 8 |
| 4 | 15 ÷ 8 = 1 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 71 | 13206 |
| 75 and 146 | 10950 |
| 174 and 152 | 13224 |
| 169 and 53 | 8957 |
| 107 and 137 | 14659 |