Least Common Multiple (LCM) of 77 and 194
The least common multiple (LCM) of 77 and 194 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 77 and 194?
First, calculate the GCD of 77 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 194 = 0 remainder 77 |
| 2 | 194 ÷ 77 = 2 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 |
|---|---|
| 105 and 72 | 2520 |
| 190 and 109 | 20710 |
| 52 and 39 | 156 |
| 163 and 104 | 16952 |
| 131 and 187 | 24497 |