Least Common Multiple (LCM) of 65 and 33
The least common multiple (LCM) of 65 and 33 is 2145.
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 65 and 33?
First, calculate the GCD of 65 and 33 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 33 = 1 remainder 32 |
| 2 | 33 ÷ 32 = 1 remainder 1 |
| 3 | 32 ÷ 1 = 32 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 167 | 33233 |
| 51 and 143 | 7293 |
| 146 and 123 | 17958 |
| 101 and 108 | 10908 |
| 144 and 185 | 26640 |