Least Common Multiple (LCM) of 194 and 100
The least common multiple (LCM) of 194 and 100 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 194 and 100?
First, calculate the GCD of 194 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 100 = 1 remainder 94 |
| 2 | 100 ÷ 94 = 1 remainder 6 |
| 3 | 94 ÷ 6 = 15 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 124 | 1860 |
| 196 and 63 | 1764 |
| 14 and 78 | 546 |
| 50 and 179 | 8950 |
| 118 and 140 | 8260 |