Least Common Multiple (LCM) of 23 and 32
The least common multiple (LCM) of 23 and 32 is 736.
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 32?
First, calculate the GCD of 23 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 32 = 0 remainder 23 |
| 2 | 32 ÷ 23 = 1 remainder 9 |
| 3 | 23 ÷ 9 = 2 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 171 | 5985 |
| 55 and 80 | 880 |
| 191 and 193 | 36863 |
| 126 and 124 | 7812 |
| 120 and 129 | 5160 |