Least Common Multiple (LCM) of 123 and 80
The least common multiple (LCM) of 123 and 80 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 123 and 80?
First, calculate the GCD of 123 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 80 = 1 remainder 43 |
| 2 | 80 ÷ 43 = 1 remainder 37 |
| 3 | 43 ÷ 37 = 1 remainder 6 |
| 4 | 37 ÷ 6 = 6 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 31 | 1736 |
| 129 and 39 | 1677 |
| 147 and 137 | 20139 |
| 182 and 21 | 546 |
| 127 and 67 | 8509 |