Least Common Multiple (LCM) of 75 and 47
The least common multiple (LCM) of 75 and 47 is 3525.
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 47?
First, calculate the GCD of 75 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 47 = 1 remainder 28 |
| 2 | 47 ÷ 28 = 1 remainder 19 |
| 3 | 28 ÷ 19 = 1 remainder 9 |
| 4 | 19 ÷ 9 = 2 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 58 | 7134 |
| 141 and 122 | 17202 |
| 167 and 19 | 3173 |
| 127 and 124 | 15748 |
| 146 and 30 | 2190 |