Least Common Multiple (LCM) of 85 and 39
The least common multiple (LCM) of 85 and 39 is 3315.
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 39?
First, calculate the GCD of 85 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 39 = 2 remainder 7 |
| 2 | 39 ÷ 7 = 5 remainder 4 |
| 3 | 7 ÷ 4 = 1 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 99 | 15543 |
| 100 and 142 | 7100 |
| 199 and 120 | 23880 |
| 161 and 64 | 10304 |
| 29 and 37 | 1073 |