Least Common Multiple (LCM) of 194 and 77
The least common multiple (LCM) of 194 and 77 is 14938.
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 77?
First, calculate the GCD of 194 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 77 = 2 remainder 40 |
| 2 | 77 ÷ 40 = 1 remainder 37 |
| 3 | 40 ÷ 37 = 1 remainder 3 |
| 4 | 37 ÷ 3 = 12 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 43 | 1376 |
| 157 and 113 | 17741 |
| 137 and 173 | 23701 |
| 190 and 114 | 570 |
| 124 and 189 | 23436 |