Least Common Multiple (LCM) of 108 and 170
The least common multiple (LCM) of 108 and 170 is 9180.
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 108 and 170?
First, calculate the GCD of 108 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 170 = 0 remainder 108 |
| 2 | 170 ÷ 108 = 1 remainder 62 |
| 3 | 108 ÷ 62 = 1 remainder 46 |
| 4 | 62 ÷ 46 = 1 remainder 16 |
| 5 | 46 ÷ 16 = 2 remainder 14 |
| 6 | 16 ÷ 14 = 1 remainder 2 |
| 7 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 96 | 16608 |
| 105 and 173 | 18165 |
| 34 and 57 | 1938 |
| 162 and 174 | 4698 |
| 13 and 11 | 143 |