Least Common Multiple (LCM) of 99 and 185
The least common multiple (LCM) of 99 and 185 is 18315.
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 99 and 185?
First, calculate the GCD of 99 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 185 = 0 remainder 99 |
| 2 | 185 ÷ 99 = 1 remainder 86 |
| 3 | 99 ÷ 86 = 1 remainder 13 |
| 4 | 86 ÷ 13 = 6 remainder 8 |
| 5 | 13 ÷ 8 = 1 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 23 | 989 |
| 192 and 132 | 2112 |
| 112 and 158 | 8848 |
| 178 and 146 | 12994 |
| 24 and 167 | 4008 |