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 |
|---|---|
| 42 and 56 | 168 |
| 169 and 143 | 1859 |
| 154 and 117 | 18018 |
| 152 and 55 | 8360 |
| 116 and 13 | 1508 |