Least Common Multiple (LCM) of 200 and 42
The least common multiple (LCM) of 200 and 42 is 4200.
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 42?
First, calculate the GCD of 200 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 42 = 4 remainder 32 |
| 2 | 42 ÷ 32 = 1 remainder 10 |
| 3 | 32 ÷ 10 = 3 remainder 2 |
| 4 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 12 | 588 |
| 80 and 83 | 6640 |
| 133 and 107 | 14231 |
| 64 and 174 | 5568 |
| 144 and 172 | 6192 |