Least Common Multiple (LCM) of 23 and 123
The least common multiple (LCM) of 23 and 123 is 2829.
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 23 and 123?
First, calculate the GCD of 23 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 123 = 0 remainder 23 |
| 2 | 123 ÷ 23 = 5 remainder 8 |
| 3 | 23 ÷ 8 = 2 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 122 | 10004 |
| 83 and 174 | 14442 |
| 78 and 200 | 7800 |
| 103 and 14 | 1442 |
| 130 and 23 | 2990 |