Least Common Multiple (LCM) of 23 and 33
The least common multiple (LCM) of 23 and 33 is 759.
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 33?
First, calculate the GCD of 23 and 33 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 33 = 0 remainder 23 |
| 2 | 33 ÷ 23 = 1 remainder 10 |
| 3 | 23 ÷ 10 = 2 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 165 | 4455 |
| 157 and 77 | 12089 |
| 21 and 146 | 3066 |
| 148 and 105 | 15540 |
| 77 and 140 | 1540 |