Least Common Multiple (LCM) of 75 and 199
The least common multiple (LCM) of 75 and 199 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 75 and 199?
First, calculate the GCD of 75 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 199 = 0 remainder 75 |
| 2 | 199 ÷ 75 = 2 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 |
|---|---|
| 47 and 172 | 8084 |
| 107 and 93 | 9951 |
| 108 and 133 | 14364 |
| 70 and 116 | 4060 |
| 153 and 182 | 27846 |