Least Common Multiple (LCM) of 74 and 198
The least common multiple (LCM) of 74 and 198 is 7326.
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 198?
First, calculate the GCD of 74 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 198 = 0 remainder 74 |
| 2 | 198 ÷ 74 = 2 remainder 50 |
| 3 | 74 ÷ 50 = 1 remainder 24 |
| 4 | 50 ÷ 24 = 2 remainder 2 |
| 5 | 24 ÷ 2 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 34 | 3706 |
| 82 and 53 | 4346 |
| 175 and 27 | 4725 |
| 176 and 159 | 27984 |
| 50 and 60 | 300 |