Least Common Multiple (LCM) of 123 and 168
The least common multiple (LCM) of 123 and 168 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 123 and 168?
First, calculate the GCD of 123 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 168 = 0 remainder 123 |
| 2 | 168 ÷ 123 = 1 remainder 45 |
| 3 | 123 ÷ 45 = 2 remainder 33 |
| 4 | 45 ÷ 33 = 1 remainder 12 |
| 5 | 33 ÷ 12 = 2 remainder 9 |
| 6 | 12 ÷ 9 = 1 remainder 3 |
| 7 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 103 | 16274 |
| 54 and 42 | 378 |
| 17 and 24 | 408 |
| 45 and 45 | 45 |
| 126 and 192 | 4032 |