Least Common Multiple (LCM) of 66 and 23
The least common multiple (LCM) of 66 and 23 is 1518.
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 66 and 23?
First, calculate the GCD of 66 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 23 = 2 remainder 20 |
| 2 | 23 ÷ 20 = 1 remainder 3 |
| 3 | 20 ÷ 3 = 6 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 36 | 2340 |
| 162 and 192 | 5184 |
| 162 and 140 | 11340 |
| 164 and 166 | 13612 |
| 75 and 194 | 14550 |