Least Common Multiple (LCM) of 170 and 69
The least common multiple (LCM) of 170 and 69 is 11730.
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 170 and 69?
First, calculate the GCD of 170 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 69 = 2 remainder 32 |
| 2 | 69 ÷ 32 = 2 remainder 5 |
| 3 | 32 ÷ 5 = 6 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 168 | 9912 |
| 163 and 151 | 24613 |
| 40 and 40 | 40 |
| 100 and 82 | 4100 |
| 176 and 43 | 7568 |