Least Common Multiple (LCM) of 198 and 77
The least common multiple (LCM) of 198 and 77 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 198 and 77?
First, calculate the GCD of 198 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 77 = 2 remainder 44 |
| 2 | 77 ÷ 44 = 1 remainder 33 |
| 3 | 44 ÷ 33 = 1 remainder 11 |
| 4 | 33 ÷ 11 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 143 | 3575 |
| 36 and 96 | 288 |
| 66 and 70 | 2310 |
| 56 and 189 | 1512 |
| 103 and 100 | 10300 |