Least Common Multiple (LCM) of 74 and 192
The least common multiple (LCM) of 74 and 192 is 7104.
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 192?
First, calculate the GCD of 74 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 192 = 0 remainder 74 |
| 2 | 192 ÷ 74 = 2 remainder 44 |
| 3 | 74 ÷ 44 = 1 remainder 30 |
| 4 | 44 ÷ 30 = 1 remainder 14 |
| 5 | 30 ÷ 14 = 2 remainder 2 |
| 6 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 191 and 41 | 7831 |
| 85 and 129 | 10965 |
| 180 and 66 | 1980 |
| 32 and 68 | 544 |
| 46 and 106 | 2438 |