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 |
|---|---|
| 111 and 42 | 1554 |
| 193 and 159 | 30687 |
| 160 and 134 | 10720 |
| 37 and 75 | 2775 |
| 126 and 102 | 2142 |