Least Common Multiple (LCM) of 48 and 200
The least common multiple (LCM) of 48 and 200 is 1200.
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 48 and 200?
First, calculate the GCD of 48 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 200 = 0 remainder 48 |
| 2 | 200 ÷ 48 = 4 remainder 8 |
| 3 | 48 ÷ 8 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 110 | 10340 |
| 145 and 112 | 16240 |
| 133 and 84 | 1596 |
| 72 and 33 | 792 |
| 175 and 135 | 4725 |