Least Common Multiple (LCM) of 47 and 75
The least common multiple (LCM) of 47 and 75 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 47 and 75?
First, calculate the GCD of 47 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 75 = 0 remainder 47 |
| 2 | 75 ÷ 47 = 1 remainder 28 |
| 3 | 47 ÷ 28 = 1 remainder 19 |
| 4 | 28 ÷ 19 = 1 remainder 9 |
| 5 | 19 ÷ 9 = 2 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 50 | 6150 |
| 132 and 43 | 5676 |
| 164 and 36 | 1476 |
| 120 and 109 | 13080 |
| 98 and 146 | 7154 |