Least Common Multiple (LCM) of 112 and 187
The least common multiple (LCM) of 112 and 187 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 112 and 187?
First, calculate the GCD of 112 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 187 = 0 remainder 112 |
| 2 | 187 ÷ 112 = 1 remainder 75 |
| 3 | 112 ÷ 75 = 1 remainder 37 |
| 4 | 75 ÷ 37 = 2 remainder 1 |
| 5 | 37 ÷ 1 = 37 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 26 and 69 | 1794 |
| 117 and 35 | 4095 |
| 117 and 114 | 4446 |
| 80 and 106 | 4240 |
| 171 and 144 | 2736 |