Least Common Multiple (LCM) of 99 and 192
The least common multiple (LCM) of 99 and 192 is 6336.
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 192?
First, calculate the GCD of 99 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 192 = 0 remainder 99 |
| 2 | 192 ÷ 99 = 1 remainder 93 |
| 3 | 99 ÷ 93 = 1 remainder 6 |
| 4 | 93 ÷ 6 = 15 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 105 | 420 |
| 169 and 137 | 23153 |
| 37 and 49 | 1813 |
| 80 and 109 | 8720 |
| 173 and 33 | 5709 |