Least Common Multiple (LCM) of 170 and 109
The least common multiple (LCM) of 170 and 109 is 18530.
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 109?
First, calculate the GCD of 170 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 109 = 1 remainder 61 |
| 2 | 109 ÷ 61 = 1 remainder 48 |
| 3 | 61 ÷ 48 = 1 remainder 13 |
| 4 | 48 ÷ 13 = 3 remainder 9 |
| 5 | 13 ÷ 9 = 1 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 190 | 12160 |
| 84 and 20 | 420 |
| 131 and 103 | 13493 |
| 160 and 146 | 11680 |
| 105 and 175 | 525 |