Least Common Multiple (LCM) of 85 and 123
The least common multiple (LCM) of 85 and 123 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 85 and 123?
First, calculate the GCD of 85 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 123 = 0 remainder 85 |
| 2 | 123 ÷ 85 = 1 remainder 38 |
| 3 | 85 ÷ 38 = 2 remainder 9 |
| 4 | 38 ÷ 9 = 4 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 34 | 3638 |
| 192 and 154 | 14784 |
| 105 and 199 | 20895 |
| 27 and 13 | 351 |
| 134 and 166 | 11122 |