Least Common Multiple (LCM) of 200 and 49
The least common multiple (LCM) of 200 and 49 is 9800.
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 49?
First, calculate the GCD of 200 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 49 = 4 remainder 4 |
| 2 | 49 ÷ 4 = 12 remainder 1 |
| 3 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 183 and 64 | 11712 |
| 18 and 30 | 90 |
| 57 and 169 | 9633 |
| 105 and 166 | 17430 |
| 192 and 158 | 15168 |