Least Common Multiple (LCM) of 75 and 115
The least common multiple (LCM) of 75 and 115 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 75 and 115?
First, calculate the GCD of 75 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 115 = 0 remainder 75 |
| 2 | 115 ÷ 75 = 1 remainder 40 |
| 3 | 75 ÷ 40 = 1 remainder 35 |
| 4 | 40 ÷ 35 = 1 remainder 5 |
| 5 | 35 ÷ 5 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 127 | 24511 |
| 74 and 106 | 3922 |
| 31 and 69 | 2139 |
| 75 and 113 | 8475 |
| 109 and 81 | 8829 |