Least Common Multiple (LCM) of 84 and 170
The least common multiple (LCM) of 84 and 170 is 7140.
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 84 and 170?
First, calculate the GCD of 84 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 170 = 0 remainder 84 |
| 2 | 170 ÷ 84 = 2 remainder 2 |
| 3 | 84 ÷ 2 = 42 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 32 | 2720 |
| 45 and 113 | 5085 |
| 186 and 186 | 186 |
| 68 and 199 | 13532 |
| 198 and 186 | 6138 |