Least Common Multiple (LCM) of 170 and 108
The least common multiple (LCM) of 170 and 108 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 170 and 108?
First, calculate the GCD of 170 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 108 = 1 remainder 62 |
| 2 | 108 ÷ 62 = 1 remainder 46 |
| 3 | 62 ÷ 46 = 1 remainder 16 |
| 4 | 46 ÷ 16 = 2 remainder 14 |
| 5 | 16 ÷ 14 = 1 remainder 2 |
| 6 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 97 | 3007 |
| 149 and 85 | 12665 |
| 31 and 17 | 527 |
| 30 and 191 | 5730 |
| 53 and 30 | 1590 |