Least Common Multiple (LCM) of 112 and 185
The least common multiple (LCM) of 112 and 185 is 20720.
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 185?
First, calculate the GCD of 112 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 185 = 0 remainder 112 |
| 2 | 185 ÷ 112 = 1 remainder 73 |
| 3 | 112 ÷ 73 = 1 remainder 39 |
| 4 | 73 ÷ 39 = 1 remainder 34 |
| 5 | 39 ÷ 34 = 1 remainder 5 |
| 6 | 34 ÷ 5 = 6 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 168 | 7896 |
| 78 and 140 | 5460 |
| 115 and 107 | 12305 |
| 158 and 191 | 30178 |
| 116 and 53 | 6148 |