Least Common Multiple (LCM) of 200 and 46
The least common multiple (LCM) of 200 and 46 is 4600.
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 46?
First, calculate the GCD of 200 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 46 = 4 remainder 16 |
| 2 | 46 ÷ 16 = 2 remainder 14 |
| 3 | 16 ÷ 14 = 1 remainder 2 |
| 4 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 75 | 3075 |
| 120 and 151 | 18120 |
| 107 and 15 | 1605 |
| 96 and 97 | 9312 |
| 137 and 174 | 23838 |