Least Common Multiple (LCM) of 199 and 174
The least common multiple (LCM) of 199 and 174 is 34626.
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 174?
First, calculate the GCD of 199 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 174 = 1 remainder 25 |
| 2 | 174 ÷ 25 = 6 remainder 24 |
| 3 | 25 ÷ 24 = 1 remainder 1 |
| 4 | 24 ÷ 1 = 24 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 124 | 3596 |
| 101 and 107 | 10807 |
| 45 and 66 | 990 |
| 14 and 24 | 168 |
| 199 and 149 | 29651 |