Least Common Multiple (LCM) of 34 and 85
The least common multiple (LCM) of 34 and 85 is 170.
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 34 and 85?
First, calculate the GCD of 34 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 85 = 0 remainder 34 |
| 2 | 85 ÷ 34 = 2 remainder 17 |
| 3 | 34 ÷ 17 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 164 | 7380 |
| 34 and 78 | 1326 |
| 157 and 49 | 7693 |
| 147 and 176 | 25872 |
| 173 and 78 | 13494 |