Least Common Multiple (LCM) of 64 and 170
The least common multiple (LCM) of 64 and 170 is 5440.
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 64 and 170?
First, calculate the GCD of 64 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 170 = 0 remainder 64 |
| 2 | 170 ÷ 64 = 2 remainder 42 |
| 3 | 64 ÷ 42 = 1 remainder 22 |
| 4 | 42 ÷ 22 = 1 remainder 20 |
| 5 | 22 ÷ 20 = 1 remainder 2 |
| 6 | 20 ÷ 2 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 129 | 17157 |
| 65 and 103 | 6695 |
| 105 and 119 | 1785 |
| 141 and 182 | 25662 |
| 17 and 155 | 2635 |