Least Common Multiple (LCM) of 96 and 125
The least common multiple (LCM) of 96 and 125 is 12000.
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 96 and 125?
First, calculate the GCD of 96 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 125 = 0 remainder 96 |
| 2 | 125 ÷ 96 = 1 remainder 29 |
| 3 | 96 ÷ 29 = 3 remainder 9 |
| 4 | 29 ÷ 9 = 3 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 48 | 48 |
| 184 and 82 | 7544 |
| 52 and 120 | 1560 |
| 27 and 132 | 1188 |
| 120 and 114 | 2280 |