Least Common Multiple (LCM) of 123 and 79
The least common multiple (LCM) of 123 and 79 is 9717.
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 79?
First, calculate the GCD of 123 and 79 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 79 = 1 remainder 44 |
| 2 | 79 ÷ 44 = 1 remainder 35 |
| 3 | 44 ÷ 35 = 1 remainder 9 |
| 4 | 35 ÷ 9 = 3 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 180 | 1800 |
| 187 and 68 | 748 |
| 123 and 173 | 21279 |
| 24 and 107 | 2568 |
| 123 and 78 | 3198 |