Least Common Multiple (LCM) of 123 and 106
The least common multiple (LCM) of 123 and 106 is 13038.
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 106?
First, calculate the GCD of 123 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 106 = 1 remainder 17 |
| 2 | 106 ÷ 17 = 6 remainder 4 |
| 3 | 17 ÷ 4 = 4 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 148 | 148 |
| 33 and 58 | 1914 |
| 133 and 58 | 7714 |
| 105 and 56 | 840 |
| 28 and 145 | 4060 |