Least Common Multiple (LCM) of 192 and 109
The least common multiple (LCM) of 192 and 109 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 192 and 109?
First, calculate the GCD of 192 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 109 = 1 remainder 83 |
| 2 | 109 ÷ 83 = 1 remainder 26 |
| 3 | 83 ÷ 26 = 3 remainder 5 |
| 4 | 26 ÷ 5 = 5 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 141 | 2115 |
| 80 and 69 | 5520 |
| 145 and 50 | 1450 |
| 186 and 121 | 22506 |
| 120 and 10 | 120 |