Least Common Multiple (LCM) of 11 and 109
The least common multiple (LCM) of 11 and 109 is 1199.
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 11 and 109?
First, calculate the GCD of 11 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 11 ÷ 109 = 0 remainder 11 |
| 2 | 109 ÷ 11 = 9 remainder 10 |
| 3 | 11 ÷ 10 = 1 remainder 1 |
| 4 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 106 | 9116 |
| 134 and 85 | 11390 |
| 188 and 34 | 3196 |
| 129 and 183 | 7869 |
| 125 and 108 | 13500 |