Least Common Multiple (LCM) of 85 and 112
The least common multiple (LCM) of 85 and 112 is 9520.
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 112?
First, calculate the GCD of 85 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 112 = 0 remainder 85 |
| 2 | 112 ÷ 85 = 1 remainder 27 |
| 3 | 85 ÷ 27 = 3 remainder 4 |
| 4 | 27 ÷ 4 = 6 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 59 | 6018 |
| 196 and 187 | 36652 |
| 180 and 85 | 3060 |
| 158 and 93 | 14694 |
| 102 and 126 | 2142 |