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 |
|---|---|
| 105 and 55 | 1155 |
| 11 and 100 | 1100 |
| 154 and 167 | 25718 |
| 112 and 31 | 3472 |
| 101 and 109 | 11009 |