Least Common Multiple (LCM) of 103 and 123
The least common multiple (LCM) of 103 and 123 is 12669.
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 103 and 123?
First, calculate the GCD of 103 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 123 = 0 remainder 103 |
| 2 | 123 ÷ 103 = 1 remainder 20 |
| 3 | 103 ÷ 20 = 5 remainder 3 |
| 4 | 20 ÷ 3 = 6 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 91 | 12376 |
| 184 and 144 | 3312 |
| 139 and 96 | 13344 |
| 154 and 192 | 14784 |
| 185 and 168 | 31080 |