Least Common Multiple (LCM) of 199 and 124
The least common multiple (LCM) of 199 and 124 is 24676.
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 124?
First, calculate the GCD of 199 and 124 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 124 = 1 remainder 75 |
| 2 | 124 ÷ 75 = 1 remainder 49 |
| 3 | 75 ÷ 49 = 1 remainder 26 |
| 4 | 49 ÷ 26 = 1 remainder 23 |
| 5 | 26 ÷ 23 = 1 remainder 3 |
| 6 | 23 ÷ 3 = 7 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 110 | 2530 |
| 15 and 182 | 2730 |
| 74 and 27 | 1998 |
| 39 and 147 | 1911 |
| 160 and 180 | 1440 |