Least Common Multiple (LCM) of 107 and 194
The least common multiple (LCM) of 107 and 194 is 20758.
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 107 and 194?
First, calculate the GCD of 107 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 194 = 0 remainder 107 |
| 2 | 194 ÷ 107 = 1 remainder 87 |
| 3 | 107 ÷ 87 = 1 remainder 20 |
| 4 | 87 ÷ 20 = 4 remainder 7 |
| 5 | 20 ÷ 7 = 2 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 111 | 7881 |
| 59 and 109 | 6431 |
| 32 and 28 | 224 |
| 126 and 167 | 21042 |
| 88 and 129 | 11352 |