Least Common Multiple (LCM) of 105 and 85
The least common multiple (LCM) of 105 and 85 is 1785.
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 105 and 85?
First, calculate the GCD of 105 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 85 = 1 remainder 20 |
| 2 | 85 ÷ 20 = 4 remainder 5 |
| 3 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 160 | 3360 |
| 172 and 152 | 6536 |
| 113 and 143 | 16159 |
| 125 and 141 | 17625 |
| 40 and 103 | 4120 |