Least Common Multiple (LCM) of 109 and 25
The least common multiple (LCM) of 109 and 25 is 2725.
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 25?
First, calculate the GCD of 109 and 25 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 25 = 4 remainder 9 |
| 2 | 25 ÷ 9 = 2 remainder 7 |
| 3 | 9 ÷ 7 = 1 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 19 | 1292 |
| 107 and 147 | 15729 |
| 49 and 142 | 6958 |
| 118 and 68 | 4012 |
| 189 and 168 | 1512 |