Least Common Multiple (LCM) of 32 and 65
The least common multiple (LCM) of 32 and 65 is 2080.
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 32 and 65?
First, calculate the GCD of 32 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 65 = 0 remainder 32 |
| 2 | 65 ÷ 32 = 2 remainder 1 |
| 3 | 32 ÷ 1 = 32 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 125 | 21125 |
| 110 and 80 | 880 |
| 100 and 128 | 3200 |
| 114 and 138 | 2622 |
| 123 and 110 | 13530 |