Least Common Multiple (LCM) of 12 and 23
The least common multiple (LCM) of 12 and 23 is 276.
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 12 and 23?
First, calculate the GCD of 12 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 23 = 0 remainder 12 |
| 2 | 23 ÷ 12 = 1 remainder 11 |
| 3 | 12 ÷ 11 = 1 remainder 1 |
| 4 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 129 | 10707 |
| 168 and 55 | 9240 |
| 161 and 105 | 2415 |
| 90 and 70 | 630 |
| 39 and 65 | 195 |