Least Common Multiple (LCM) of 199 and 67
The least common multiple (LCM) of 199 and 67 is 13333.
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 199 and 67?
First, calculate the GCD of 199 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 67 = 2 remainder 65 |
| 2 | 67 ÷ 65 = 1 remainder 2 |
| 3 | 65 ÷ 2 = 32 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 166 | 22078 |
| 121 and 112 | 13552 |
| 191 and 43 | 8213 |
| 192 and 105 | 6720 |
| 190 and 111 | 21090 |