Least Common Multiple (LCM) of 10 and 23
The least common multiple (LCM) of 10 and 23 is 230.
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 10 and 23?
First, calculate the GCD of 10 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 10 ÷ 23 = 0 remainder 10 |
| 2 | 23 ÷ 10 = 2 remainder 3 |
| 3 | 10 ÷ 3 = 3 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 138 | 4830 |
| 56 and 181 | 10136 |
| 145 and 54 | 7830 |
| 14 and 25 | 350 |
| 188 and 145 | 27260 |