Least Common Multiple (LCM) of 64 and 125
The least common multiple (LCM) of 64 and 125 is 8000.
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 125?
First, calculate the GCD of 64 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 125 = 0 remainder 64 |
| 2 | 125 ÷ 64 = 1 remainder 61 |
| 3 | 64 ÷ 61 = 1 remainder 3 |
| 4 | 61 ÷ 3 = 20 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 105 | 19320 |
| 178 and 44 | 3916 |
| 188 and 102 | 9588 |
| 112 and 51 | 5712 |
| 175 and 70 | 350 |