Least Common Multiple (LCM) of 194 and 71
The least common multiple (LCM) of 194 and 71 is 13774.
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 194 and 71?
First, calculate the GCD of 194 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 71 = 2 remainder 52 |
| 2 | 71 ÷ 52 = 1 remainder 19 |
| 3 | 52 ÷ 19 = 2 remainder 14 |
| 4 | 19 ÷ 14 = 1 remainder 5 |
| 5 | 14 ÷ 5 = 2 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 28 and 133 | 532 |
| 65 and 48 | 3120 |
| 123 and 161 | 19803 |
| 187 and 192 | 35904 |
| 172 and 106 | 9116 |