Least Common Multiple (LCM) of 64 and 105
The least common multiple (LCM) of 64 and 105 is 6720.
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 105?
First, calculate the GCD of 64 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 105 = 0 remainder 64 |
| 2 | 105 ÷ 64 = 1 remainder 41 |
| 3 | 64 ÷ 41 = 1 remainder 23 |
| 4 | 41 ÷ 23 = 1 remainder 18 |
| 5 | 23 ÷ 18 = 1 remainder 5 |
| 6 | 18 ÷ 5 = 3 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 71 | 9088 |
| 89 and 49 | 4361 |
| 16 and 153 | 2448 |
| 133 and 160 | 21280 |
| 154 and 86 | 6622 |