Least Common Multiple (LCM) of 109 and 170
The least common multiple (LCM) of 109 and 170 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 109 and 170?
First, calculate the GCD of 109 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 170 = 0 remainder 109 |
| 2 | 170 ÷ 109 = 1 remainder 61 |
| 3 | 109 ÷ 61 = 1 remainder 48 |
| 4 | 61 ÷ 48 = 1 remainder 13 |
| 5 | 48 ÷ 13 = 3 remainder 9 |
| 6 | 13 ÷ 9 = 1 remainder 4 |
| 7 | 9 ÷ 4 = 2 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 113 | 21244 |
| 172 and 164 | 7052 |
| 44 and 82 | 1804 |
| 165 and 188 | 31020 |
| 113 and 145 | 16385 |