Least Common Multiple (LCM) of 23 and 39
The least common multiple (LCM) of 23 and 39 is 897.
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 39?
First, calculate the GCD of 23 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 39 = 0 remainder 23 |
| 2 | 39 ÷ 23 = 1 remainder 16 |
| 3 | 23 ÷ 16 = 1 remainder 7 |
| 4 | 16 ÷ 7 = 2 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 92 | 10396 |
| 126 and 145 | 18270 |
| 90 and 162 | 810 |
| 193 and 124 | 23932 |
| 53 and 183 | 9699 |