Least Common Multiple (LCM) of 185 and 112
The least common multiple (LCM) of 185 and 112 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 185 and 112?
First, calculate the GCD of 185 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 112 = 1 remainder 73 |
| 2 | 112 ÷ 73 = 1 remainder 39 |
| 3 | 73 ÷ 39 = 1 remainder 34 |
| 4 | 39 ÷ 34 = 1 remainder 5 |
| 5 | 34 ÷ 5 = 6 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 63 | 126 |
| 116 and 83 | 9628 |
| 140 and 199 | 27860 |
| 74 and 165 | 12210 |
| 34 and 157 | 5338 |