Least Common Multiple (LCM) of 65 and 191
The least common multiple (LCM) of 65 and 191 is 12415.
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 191?
First, calculate the GCD of 65 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 191 = 0 remainder 65 |
| 2 | 191 ÷ 65 = 2 remainder 61 |
| 3 | 65 ÷ 61 = 1 remainder 4 |
| 4 | 61 ÷ 4 = 15 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 42 | 1050 |
| 191 and 117 | 22347 |
| 57 and 19 | 57 |
| 10 and 167 | 1670 |
| 132 and 78 | 1716 |