Least Common Multiple (LCM) of 30 and 194
The least common multiple (LCM) of 30 and 194 is 2910.
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 30 and 194?
First, calculate the GCD of 30 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 194 = 0 remainder 30 |
| 2 | 194 ÷ 30 = 6 remainder 14 |
| 3 | 30 ÷ 14 = 2 remainder 2 |
| 4 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 80 | 720 |
| 62 and 115 | 7130 |
| 136 and 78 | 5304 |
| 129 and 31 | 3999 |
| 162 and 189 | 1134 |