Least Common Multiple (LCM) of 187 and 112
The least common multiple (LCM) of 187 and 112 is 20944.
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 187 and 112?
First, calculate the GCD of 187 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 187 ÷ 112 = 1 remainder 75 |
| 2 | 112 ÷ 75 = 1 remainder 37 |
| 3 | 75 ÷ 37 = 2 remainder 1 |
| 4 | 37 ÷ 1 = 37 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 36 | 1044 |
| 185 and 48 | 8880 |
| 84 and 180 | 1260 |
| 155 and 37 | 5735 |
| 126 and 128 | 8064 |