Least Common Multiple (LCM) of 65 and 164
The least common multiple (LCM) of 65 and 164 is 10660.
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 164?
First, calculate the GCD of 65 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 164 = 0 remainder 65 |
| 2 | 164 ÷ 65 = 2 remainder 34 |
| 3 | 65 ÷ 34 = 1 remainder 31 |
| 4 | 34 ÷ 31 = 1 remainder 3 |
| 5 | 31 ÷ 3 = 10 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 137 | 8768 |
| 71 and 95 | 6745 |
| 16 and 22 | 176 |
| 140 and 57 | 7980 |
| 17 and 152 | 2584 |