Least Common Multiple (LCM) of 48 and 125
The least common multiple (LCM) of 48 and 125 is 6000.
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 48 and 125?
First, calculate the GCD of 48 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 125 = 0 remainder 48 |
| 2 | 125 ÷ 48 = 2 remainder 29 |
| 3 | 48 ÷ 29 = 1 remainder 19 |
| 4 | 29 ÷ 19 = 1 remainder 10 |
| 5 | 19 ÷ 10 = 1 remainder 9 |
| 6 | 10 ÷ 9 = 1 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 180 | 24660 |
| 189 and 178 | 33642 |
| 147 and 150 | 7350 |
| 169 and 165 | 27885 |
| 179 and 54 | 9666 |