Least Common Multiple (LCM) of 105 and 125
The least common multiple (LCM) of 105 and 125 is 2625.
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 105 and 125?
First, calculate the GCD of 105 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 125 = 0 remainder 105 |
| 2 | 125 ÷ 105 = 1 remainder 20 |
| 3 | 105 ÷ 20 = 5 remainder 5 |
| 4 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 105 | 210 |
| 103 and 200 | 20600 |
| 190 and 183 | 34770 |
| 108 and 113 | 12204 |
| 140 and 32 | 1120 |