Least Common Multiple (LCM) of 108 and 64
The least common multiple (LCM) of 108 and 64 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 108 and 64?
First, calculate the GCD of 108 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 64 = 1 remainder 44 |
| 2 | 64 ÷ 44 = 1 remainder 20 |
| 3 | 44 ÷ 20 = 2 remainder 4 |
| 4 | 20 ÷ 4 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 169 | 32448 |
| 195 and 183 | 11895 |
| 135 and 23 | 3105 |
| 106 and 193 | 20458 |
| 83 and 30 | 2490 |