Least Common Multiple (LCM) of 74 and 199
The least common multiple (LCM) of 74 and 199 is 14726.
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 74 and 199?
First, calculate the GCD of 74 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 199 = 0 remainder 74 |
| 2 | 199 ÷ 74 = 2 remainder 51 |
| 3 | 74 ÷ 51 = 1 remainder 23 |
| 4 | 51 ÷ 23 = 2 remainder 5 |
| 5 | 23 ÷ 5 = 4 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 188 | 15980 |
| 18 and 147 | 882 |
| 149 and 109 | 16241 |
| 89 and 167 | 14863 |
| 29 and 92 | 2668 |