Least Common Multiple (LCM) of 47 and 135
The least common multiple (LCM) of 47 and 135 is 6345.
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 135?
First, calculate the GCD of 47 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 135 = 0 remainder 47 |
| 2 | 135 ÷ 47 = 2 remainder 41 |
| 3 | 47 ÷ 41 = 1 remainder 6 |
| 4 | 41 ÷ 6 = 6 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 52 | 3172 |
| 42 and 177 | 2478 |
| 172 and 17 | 2924 |
| 165 and 115 | 3795 |
| 71 and 48 | 3408 |