Least Common Multiple (LCM) of 23 and 109
The least common multiple (LCM) of 23 and 109 is 2507.
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 23 and 109?
First, calculate the GCD of 23 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 109 = 0 remainder 23 |
| 2 | 109 ÷ 23 = 4 remainder 17 |
| 3 | 23 ÷ 17 = 1 remainder 6 |
| 4 | 17 ÷ 6 = 2 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 105 | 17745 |
| 188 and 13 | 2444 |
| 73 and 165 | 12045 |
| 38 and 185 | 7030 |
| 73 and 167 | 12191 |