Least Common Multiple (LCM) of 123 and 192
The least common multiple (LCM) of 123 and 192 is 7872.
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 123 and 192?
First, calculate the GCD of 123 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 192 = 0 remainder 123 |
| 2 | 192 ÷ 123 = 1 remainder 69 |
| 3 | 123 ÷ 69 = 1 remainder 54 |
| 4 | 69 ÷ 54 = 1 remainder 15 |
| 5 | 54 ÷ 15 = 3 remainder 9 |
| 6 | 15 ÷ 9 = 1 remainder 6 |
| 7 | 9 ÷ 6 = 1 remainder 3 |
| 8 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 95 | 1615 |
| 45 and 161 | 7245 |
| 95 and 90 | 1710 |
| 102 and 189 | 6426 |
| 77 and 102 | 7854 |