Least Common Multiple (LCM) of 115 and 75
The least common multiple (LCM) of 115 and 75 is 1725.
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 115 and 75?
First, calculate the GCD of 115 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 75 = 1 remainder 40 |
| 2 | 75 ÷ 40 = 1 remainder 35 |
| 3 | 40 ÷ 35 = 1 remainder 5 |
| 4 | 35 ÷ 5 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 66 | 2310 |
| 126 and 29 | 3654 |
| 103 and 40 | 4120 |
| 153 and 190 | 29070 |
| 122 and 164 | 10004 |