Least Common Multiple (LCM) of 65 and 199
The least common multiple (LCM) of 65 and 199 is 12935.
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 199?
First, calculate the GCD of 65 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 199 = 0 remainder 65 |
| 2 | 199 ÷ 65 = 3 remainder 4 |
| 3 | 65 ÷ 4 = 16 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 82 | 2706 |
| 96 and 170 | 8160 |
| 117 and 151 | 17667 |
| 88 and 80 | 880 |
| 107 and 79 | 8453 |