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 |
|---|---|
| 141 and 11 | 1551 |
| 106 and 44 | 2332 |
| 76 and 137 | 10412 |
| 167 and 112 | 18704 |
| 105 and 49 | 735 |