Least Common Multiple (LCM) of 123 and 199
The least common multiple (LCM) of 123 and 199 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 123 and 199?
First, calculate the GCD of 123 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 199 = 0 remainder 123 |
| 2 | 199 ÷ 123 = 1 remainder 76 |
| 3 | 123 ÷ 76 = 1 remainder 47 |
| 4 | 76 ÷ 47 = 1 remainder 29 |
| 5 | 47 ÷ 29 = 1 remainder 18 |
| 6 | 29 ÷ 18 = 1 remainder 11 |
| 7 | 18 ÷ 11 = 1 remainder 7 |
| 8 | 11 ÷ 7 = 1 remainder 4 |
| 9 | 7 ÷ 4 = 1 remainder 3 |
| 10 | 4 ÷ 3 = 1 remainder 1 |
| 11 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 47 | 8037 |
| 42 and 54 | 378 |
| 186 and 36 | 1116 |
| 173 and 140 | 24220 |
| 59 and 104 | 6136 |