Least Common Multiple (LCM) of 164 and 65
The least common multiple (LCM) of 164 and 65 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 164 and 65?
First, calculate the GCD of 164 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 65 = 2 remainder 34 |
| 2 | 65 ÷ 34 = 1 remainder 31 |
| 3 | 34 ÷ 31 = 1 remainder 3 |
| 4 | 31 ÷ 3 = 10 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 144 | 144 |
| 56 and 146 | 4088 |
| 199 and 44 | 8756 |
| 178 and 55 | 9790 |
| 124 and 155 | 620 |