Least Common Multiple (LCM) of 123 and 85
The least common multiple (LCM) of 123 and 85 is 10455.
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 85?
First, calculate the GCD of 123 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 85 = 1 remainder 38 |
| 2 | 85 ÷ 38 = 2 remainder 9 |
| 3 | 38 ÷ 9 = 4 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 90 | 990 |
| 56 and 16 | 112 |
| 49 and 144 | 7056 |
| 145 and 142 | 20590 |
| 47 and 31 | 1457 |