Least Common Multiple (LCM) of 85 and 100
The least common multiple (LCM) of 85 and 100 is 1700.
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 100?
First, calculate the GCD of 85 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 100 = 0 remainder 85 |
| 2 | 100 ÷ 85 = 1 remainder 15 |
| 3 | 85 ÷ 15 = 5 remainder 10 |
| 4 | 15 ÷ 10 = 1 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 55 | 5830 |
| 100 and 152 | 3800 |
| 163 and 164 | 26732 |
| 90 and 35 | 630 |
| 195 and 37 | 7215 |