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 |
|---|---|
| 90 and 162 | 810 |
| 184 and 60 | 2760 |
| 96 and 141 | 4512 |
| 118 and 37 | 4366 |
| 136 and 57 | 7752 |