Least Common Multiple (LCM) of 109 and 192
The least common multiple (LCM) of 109 and 192 is 20928.
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 109 and 192?
First, calculate the GCD of 109 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 192 = 0 remainder 109 |
| 2 | 192 ÷ 109 = 1 remainder 83 |
| 3 | 109 ÷ 83 = 1 remainder 26 |
| 4 | 83 ÷ 26 = 3 remainder 5 |
| 5 | 26 ÷ 5 = 5 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 179 | 35621 |
| 17 and 115 | 1955 |
| 146 and 145 | 21170 |
| 165 and 128 | 21120 |
| 53 and 30 | 1590 |