Least Common Multiple (LCM) of 199 and 123
The least common multiple (LCM) of 199 and 123 is 24477.
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 123?
First, calculate the GCD of 199 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 123 = 1 remainder 76 |
| 2 | 123 ÷ 76 = 1 remainder 47 |
| 3 | 76 ÷ 47 = 1 remainder 29 |
| 4 | 47 ÷ 29 = 1 remainder 18 |
| 5 | 29 ÷ 18 = 1 remainder 11 |
| 6 | 18 ÷ 11 = 1 remainder 7 |
| 7 | 11 ÷ 7 = 1 remainder 4 |
| 8 | 7 ÷ 4 = 1 remainder 3 |
| 9 | 4 ÷ 3 = 1 remainder 1 |
| 10 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 157 | 26847 |
| 133 and 156 | 20748 |
| 141 and 38 | 5358 |
| 173 and 46 | 7958 |
| 121 and 189 | 22869 |