Least Common Multiple (LCM) of 112 and 100
The least common multiple (LCM) of 112 and 100 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 100?
First, calculate the GCD of 112 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 100 = 1 remainder 12 |
| 2 | 100 ÷ 12 = 8 remainder 4 |
| 3 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 149 | 29800 |
| 86 and 165 | 14190 |
| 96 and 155 | 14880 |
| 175 and 166 | 29050 |
| 170 and 150 | 2550 |