Least Common Multiple (LCM) of 134 and 198
The least common multiple (LCM) of 134 and 198 is 13266.
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 134 and 198?
First, calculate the GCD of 134 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 134 ÷ 198 = 0 remainder 134 |
| 2 | 198 ÷ 134 = 1 remainder 64 |
| 3 | 134 ÷ 64 = 2 remainder 6 |
| 4 | 64 ÷ 6 = 10 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 18 | 450 |
| 175 and 49 | 1225 |
| 100 and 135 | 2700 |
| 40 and 69 | 2760 |
| 44 and 175 | 7700 |