Least Common Multiple (LCM) of 109 and 95
The least common multiple (LCM) of 109 and 95 is 10355.
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 95?
First, calculate the GCD of 109 and 95 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 95 = 1 remainder 14 |
| 2 | 95 ÷ 14 = 6 remainder 11 |
| 3 | 14 ÷ 11 = 1 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 186 | 24366 |
| 68 and 143 | 9724 |
| 132 and 56 | 1848 |
| 163 and 142 | 23146 |
| 142 and 132 | 9372 |