Least Common Multiple (LCM) of 199 and 175
The least common multiple (LCM) of 199 and 175 is 34825.
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 175?
First, calculate the GCD of 199 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 175 = 1 remainder 24 |
| 2 | 175 ÷ 24 = 7 remainder 7 |
| 3 | 24 ÷ 7 = 3 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 61 | 2623 |
| 179 and 84 | 15036 |
| 96 and 61 | 5856 |
| 107 and 120 | 12840 |
| 90 and 84 | 1260 |