Least Common Multiple (LCM) of 74 and 194
The least common multiple (LCM) of 74 and 194 is 7178.
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 194?
First, calculate the GCD of 74 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 194 = 0 remainder 74 |
| 2 | 194 ÷ 74 = 2 remainder 46 |
| 3 | 74 ÷ 46 = 1 remainder 28 |
| 4 | 46 ÷ 28 = 1 remainder 18 |
| 5 | 28 ÷ 18 = 1 remainder 10 |
| 6 | 18 ÷ 10 = 1 remainder 8 |
| 7 | 10 ÷ 8 = 1 remainder 2 |
| 8 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 114 | 16986 |
| 79 and 156 | 12324 |
| 52 and 37 | 1924 |
| 69 and 84 | 1932 |
| 155 and 180 | 5580 |