Least Common Multiple (LCM) of 125 and 64
The least common multiple (LCM) of 125 and 64 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 125 and 64?
First, calculate the GCD of 125 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 64 = 1 remainder 61 |
| 2 | 64 ÷ 61 = 1 remainder 3 |
| 3 | 61 ÷ 3 = 20 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 13 | 1287 |
| 147 and 37 | 5439 |
| 106 and 144 | 7632 |
| 192 and 73 | 14016 |
| 83 and 99 | 8217 |