Least Common Multiple (LCM) of 199 and 75
The least common multiple (LCM) of 199 and 75 is 14925.
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 75?
First, calculate the GCD of 199 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 75 = 2 remainder 49 |
| 2 | 75 ÷ 49 = 1 remainder 26 |
| 3 | 49 ÷ 26 = 1 remainder 23 |
| 4 | 26 ÷ 23 = 1 remainder 3 |
| 5 | 23 ÷ 3 = 7 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 110 | 330 |
| 159 and 59 | 9381 |
| 159 and 64 | 10176 |
| 30 and 44 | 660 |
| 10 and 122 | 610 |