Least Common Multiple (LCM) of 194 and 117
The least common multiple (LCM) of 194 and 117 is 22698.
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 117?
First, calculate the GCD of 194 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 117 = 1 remainder 77 |
| 2 | 117 ÷ 77 = 1 remainder 40 |
| 3 | 77 ÷ 40 = 1 remainder 37 |
| 4 | 40 ÷ 37 = 1 remainder 3 |
| 5 | 37 ÷ 3 = 12 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 10 | 530 |
| 191 and 30 | 5730 |
| 128 and 118 | 7552 |
| 80 and 41 | 3280 |
| 40 and 63 | 2520 |