Least Common Multiple (LCM) of 80 and 123
The least common multiple (LCM) of 80 and 123 is 9840.
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 80 and 123?
First, calculate the GCD of 80 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 123 = 0 remainder 80 |
| 2 | 123 ÷ 80 = 1 remainder 43 |
| 3 | 80 ÷ 43 = 1 remainder 37 |
| 4 | 43 ÷ 37 = 1 remainder 6 |
| 5 | 37 ÷ 6 = 6 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 126 | 1260 |
| 108 and 107 | 11556 |
| 92 and 187 | 17204 |
| 183 and 107 | 19581 |
| 51 and 44 | 2244 |