Least Common Multiple (LCM) of 64 and 108
The least common multiple (LCM) of 64 and 108 is 1728.
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 108?
First, calculate the GCD of 64 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 108 = 0 remainder 64 |
| 2 | 108 ÷ 64 = 1 remainder 44 |
| 3 | 64 ÷ 44 = 1 remainder 20 |
| 4 | 44 ÷ 20 = 2 remainder 4 |
| 5 | 20 ÷ 4 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 40 | 120 |
| 87 and 71 | 6177 |
| 57 and 160 | 9120 |
| 74 and 141 | 10434 |
| 25 and 197 | 4925 |