Least Common Multiple (LCM) of 198 and 67
The least common multiple (LCM) of 198 and 67 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 198 and 67?
First, calculate the GCD of 198 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 67 = 2 remainder 64 |
| 2 | 67 ÷ 64 = 1 remainder 3 |
| 3 | 64 ÷ 3 = 21 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 69 | 10074 |
| 42 and 146 | 3066 |
| 181 and 25 | 4525 |
| 11 and 122 | 1342 |
| 113 and 195 | 22035 |