Least Common Multiple (LCM) of 105 and 192
The least common multiple (LCM) of 105 and 192 is 6720.
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 105 and 192?
First, calculate the GCD of 105 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 192 = 0 remainder 105 |
| 2 | 192 ÷ 105 = 1 remainder 87 |
| 3 | 105 ÷ 87 = 1 remainder 18 |
| 4 | 87 ÷ 18 = 4 remainder 15 |
| 5 | 18 ÷ 15 = 1 remainder 3 |
| 6 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 138 | 690 |
| 125 and 20 | 500 |
| 127 and 91 | 11557 |
| 37 and 110 | 4070 |
| 40 and 60 | 120 |