Least Common Multiple (LCM) of 77 and 198
The least common multiple (LCM) of 77 and 198 is 1386.
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 198?
First, calculate the GCD of 77 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 198 = 0 remainder 77 |
| 2 | 198 ÷ 77 = 2 remainder 44 |
| 3 | 77 ÷ 44 = 1 remainder 33 |
| 4 | 44 ÷ 33 = 1 remainder 11 |
| 5 | 33 ÷ 11 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 69 | 9384 |
| 181 and 105 | 19005 |
| 138 and 144 | 3312 |
| 11 and 193 | 2123 |
| 83 and 78 | 6474 |