Least Common Multiple (LCM) of 112 and 50
The least common multiple (LCM) of 112 and 50 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 112 and 50?
First, calculate the GCD of 112 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 50 = 2 remainder 12 |
| 2 | 50 ÷ 12 = 4 remainder 2 |
| 3 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 145 | 2610 |
| 175 and 71 | 12425 |
| 16 and 197 | 3152 |
| 51 and 99 | 1683 |
| 97 and 26 | 2522 |