Least Common Multiple (LCM) of 169 and 110
The least common multiple (LCM) of 169 and 110 is 18590.
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 169 and 110?
First, calculate the GCD of 169 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 110 = 1 remainder 59 |
| 2 | 110 ÷ 59 = 1 remainder 51 |
| 3 | 59 ÷ 51 = 1 remainder 8 |
| 4 | 51 ÷ 8 = 6 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 191 | 35908 |
| 165 and 70 | 2310 |
| 145 and 180 | 5220 |
| 25 and 34 | 850 |
| 186 and 189 | 11718 |