Least Common Multiple (LCM) of 200 and 67
The least common multiple (LCM) of 200 and 67 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 200 and 67?
First, calculate the GCD of 200 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 67 = 2 remainder 66 |
| 2 | 67 ÷ 66 = 1 remainder 1 |
| 3 | 66 ÷ 1 = 66 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 72 | 1800 |
| 122 and 174 | 10614 |
| 132 and 40 | 1320 |
| 28 and 179 | 5012 |
| 12 and 15 | 60 |