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 |
|---|---|
| 102 and 103 | 10506 |
| 135 and 167 | 22545 |
| 174 and 31 | 5394 |
| 151 and 104 | 15704 |
| 174 and 70 | 6090 |