Least Common Multiple (LCM) of 99 and 163
The least common multiple (LCM) of 99 and 163 is 16137.
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 163?
First, calculate the GCD of 99 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 163 = 0 remainder 99 |
| 2 | 163 ÷ 99 = 1 remainder 64 |
| 3 | 99 ÷ 64 = 1 remainder 35 |
| 4 | 64 ÷ 35 = 1 remainder 29 |
| 5 | 35 ÷ 29 = 1 remainder 6 |
| 6 | 29 ÷ 6 = 4 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 183 | 3660 |
| 109 and 174 | 18966 |
| 109 and 180 | 19620 |
| 105 and 18 | 630 |
| 172 and 149 | 25628 |