Least Common Multiple (LCM) of 47 and 161
The least common multiple (LCM) of 47 and 161 is 7567.
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 161?
First, calculate the GCD of 47 and 161 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 161 = 0 remainder 47 |
| 2 | 161 ÷ 47 = 3 remainder 20 |
| 3 | 47 ÷ 20 = 2 remainder 7 |
| 4 | 20 ÷ 7 = 2 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 20 | 180 |
| 142 and 105 | 14910 |
| 122 and 138 | 8418 |
| 91 and 140 | 1820 |
| 169 and 191 | 32279 |