Least Common Multiple (LCM) of 23 and 104
The least common multiple (LCM) of 23 and 104 is 2392.
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 104?
First, calculate the GCD of 23 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 104 = 0 remainder 23 |
| 2 | 104 ÷ 23 = 4 remainder 12 |
| 3 | 23 ÷ 12 = 1 remainder 11 |
| 4 | 12 ÷ 11 = 1 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 152 | 20824 |
| 54 and 179 | 9666 |
| 116 and 165 | 19140 |
| 186 and 184 | 17112 |
| 72 and 135 | 1080 |