Least Common Multiple (LCM) of 39 and 64
The least common multiple (LCM) of 39 and 64 is 2496.
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 39 and 64?
First, calculate the GCD of 39 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 39 ÷ 64 = 0 remainder 39 |
| 2 | 64 ÷ 39 = 1 remainder 25 |
| 3 | 39 ÷ 25 = 1 remainder 14 |
| 4 | 25 ÷ 14 = 1 remainder 11 |
| 5 | 14 ÷ 11 = 1 remainder 3 |
| 6 | 11 ÷ 3 = 3 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 141 | 13677 |
| 105 and 137 | 14385 |
| 167 and 196 | 32732 |
| 152 and 84 | 3192 |
| 19 and 16 | 304 |