Least Common Multiple (LCM) of 100 and 194
The least common multiple (LCM) of 100 and 194 is 9700.
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 100 and 194?
First, calculate the GCD of 100 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 194 = 0 remainder 100 |
| 2 | 194 ÷ 100 = 1 remainder 94 |
| 3 | 100 ÷ 94 = 1 remainder 6 |
| 4 | 94 ÷ 6 = 15 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 100 | 1100 |
| 105 and 45 | 315 |
| 132 and 85 | 11220 |
| 196 and 12 | 588 |
| 163 and 133 | 21679 |