Least Common Multiple (LCM) of 112 and 125
The least common multiple (LCM) of 112 and 125 is 14000.
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 125?
First, calculate the GCD of 112 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 125 = 0 remainder 112 |
| 2 | 125 ÷ 112 = 1 remainder 13 |
| 3 | 112 ÷ 13 = 8 remainder 8 |
| 4 | 13 ÷ 8 = 1 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 131 | 14672 |
| 91 and 24 | 2184 |
| 14 and 17 | 238 |
| 187 and 31 | 5797 |
| 75 and 48 | 1200 |