Least Common Multiple (LCM) of 99 and 186
The least common multiple (LCM) of 99 and 186 is 6138.
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 186?
First, calculate the GCD of 99 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 186 = 0 remainder 99 |
| 2 | 186 ÷ 99 = 1 remainder 87 |
| 3 | 99 ÷ 87 = 1 remainder 12 |
| 4 | 87 ÷ 12 = 7 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 57 | 3420 |
| 104 and 74 | 3848 |
| 132 and 19 | 2508 |
| 60 and 31 | 1860 |
| 54 and 131 | 7074 |