Least Common Multiple (LCM) of 192 and 123
The least common multiple (LCM) of 192 and 123 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 192 and 123?
First, calculate the GCD of 192 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 123 = 1 remainder 69 |
| 2 | 123 ÷ 69 = 1 remainder 54 |
| 3 | 69 ÷ 54 = 1 remainder 15 |
| 4 | 54 ÷ 15 = 3 remainder 9 |
| 5 | 15 ÷ 9 = 1 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 32 | 672 |
| 60 and 78 | 780 |
| 139 and 104 | 14456 |
| 184 and 82 | 7544 |
| 20 and 73 | 1460 |