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 |
|---|---|
| 122 and 112 | 6832 |
| 42 and 55 | 2310 |
| 118 and 56 | 3304 |
| 111 and 106 | 11766 |
| 91 and 34 | 3094 |