Least Common Multiple (LCM) of 67 and 200
The least common multiple (LCM) of 67 and 200 is 13400.
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 200?
First, calculate the GCD of 67 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 200 = 0 remainder 67 |
| 2 | 200 ÷ 67 = 2 remainder 66 |
| 3 | 67 ÷ 66 = 1 remainder 1 |
| 4 | 66 ÷ 1 = 66 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 41 | 4756 |
| 188 and 165 | 31020 |
| 200 and 171 | 34200 |
| 176 and 179 | 31504 |
| 22 and 194 | 2134 |