Least Common Multiple (LCM) of 65 and 133
The least common multiple (LCM) of 65 and 133 is 8645.
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 133?
First, calculate the GCD of 65 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 133 = 0 remainder 65 |
| 2 | 133 ÷ 65 = 2 remainder 3 |
| 3 | 65 ÷ 3 = 21 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 70 | 1680 |
| 70 and 150 | 1050 |
| 179 and 85 | 15215 |
| 186 and 15 | 930 |
| 10 and 40 | 40 |