Least Common Multiple (LCM) of 168 and 123
The least common multiple (LCM) of 168 and 123 is 6888.
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 168 and 123?
First, calculate the GCD of 168 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 123 = 1 remainder 45 |
| 2 | 123 ÷ 45 = 2 remainder 33 |
| 3 | 45 ÷ 33 = 1 remainder 12 |
| 4 | 33 ÷ 12 = 2 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 17 | 2584 |
| 36 and 46 | 828 |
| 197 and 133 | 26201 |
| 103 and 91 | 9373 |
| 114 and 174 | 3306 |