Least Common Multiple (LCM) of 113 and 75
The least common multiple (LCM) of 113 and 75 is 8475.
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 113 and 75?
First, calculate the GCD of 113 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 75 = 1 remainder 38 |
| 2 | 75 ÷ 38 = 1 remainder 37 |
| 3 | 38 ÷ 37 = 1 remainder 1 |
| 4 | 37 ÷ 1 = 37 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 103 | 14935 |
| 159 and 180 | 9540 |
| 59 and 45 | 2655 |
| 128 and 119 | 15232 |
| 40 and 68 | 680 |