Least Common Multiple (LCM) of 200 and 112
The least common multiple (LCM) of 200 and 112 is 2800.
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 112?
First, calculate the GCD of 200 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 112 = 1 remainder 88 |
| 2 | 112 ÷ 88 = 1 remainder 24 |
| 3 | 88 ÷ 24 = 3 remainder 16 |
| 4 | 24 ÷ 16 = 1 remainder 8 |
| 5 | 16 ÷ 8 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 91 | 455 |
| 162 and 113 | 18306 |
| 127 and 29 | 3683 |
| 172 and 102 | 8772 |
| 57 and 17 | 969 |