Least Common Multiple (LCM) of 16 and 125
The least common multiple (LCM) of 16 and 125 is 2000.
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 16 and 125?
First, calculate the GCD of 16 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 125 = 0 remainder 16 |
| 2 | 125 ÷ 16 = 7 remainder 13 |
| 3 | 16 ÷ 13 = 1 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 140 | 420 |
| 110 and 190 | 2090 |
| 39 and 76 | 2964 |
| 175 and 107 | 18725 |
| 107 and 158 | 16906 |