Least Common Multiple (LCM) of 105 and 170
The least common multiple (LCM) of 105 and 170 is 3570.
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 105 and 170?
First, calculate the GCD of 105 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 170 = 0 remainder 105 |
| 2 | 170 ÷ 105 = 1 remainder 65 |
| 3 | 105 ÷ 65 = 1 remainder 40 |
| 4 | 65 ÷ 40 = 1 remainder 25 |
| 5 | 40 ÷ 25 = 1 remainder 15 |
| 6 | 25 ÷ 15 = 1 remainder 10 |
| 7 | 15 ÷ 10 = 1 remainder 5 |
| 8 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 33 | 5775 |
| 60 and 40 | 120 |
| 16 and 110 | 880 |
| 35 and 18 | 630 |
| 118 and 164 | 9676 |