Least Common Multiple (LCM) of 64 and 75
The least common multiple (LCM) of 64 and 75 is 4800.
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 75?
First, calculate the GCD of 64 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 75 = 0 remainder 64 |
| 2 | 75 ÷ 64 = 1 remainder 11 |
| 3 | 64 ÷ 11 = 5 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 109 | 12426 |
| 169 and 76 | 12844 |
| 176 and 153 | 26928 |
| 64 and 31 | 1984 |
| 59 and 103 | 6077 |