Least Common Multiple (LCM) of 67 and 199
The least common multiple (LCM) of 67 and 199 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 67 and 199?
First, calculate the GCD of 67 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 199 = 0 remainder 67 |
| 2 | 199 ÷ 67 = 2 remainder 65 |
| 3 | 67 ÷ 65 = 1 remainder 2 |
| 4 | 65 ÷ 2 = 32 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 74 | 4810 |
| 24 and 158 | 1896 |
| 108 and 54 | 108 |
| 33 and 122 | 4026 |
| 14 and 87 | 1218 |