Least Common Multiple (LCM) of 110 and 169
The least common multiple (LCM) of 110 and 169 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 110 and 169?
First, calculate the GCD of 110 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 169 = 0 remainder 110 |
| 2 | 169 ÷ 110 = 1 remainder 59 |
| 3 | 110 ÷ 59 = 1 remainder 51 |
| 4 | 59 ÷ 51 = 1 remainder 8 |
| 5 | 51 ÷ 8 = 6 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 106 | 5088 |
| 67 and 105 | 7035 |
| 195 and 133 | 25935 |
| 139 and 60 | 8340 |
| 11 and 38 | 418 |