Least Common Multiple (LCM) of 13 and 161
The least common multiple (LCM) of 13 and 161 is 2093.
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 13 and 161?
First, calculate the GCD of 13 and 161 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 161 = 0 remainder 13 |
| 2 | 161 ÷ 13 = 12 remainder 5 |
| 3 | 13 ÷ 5 = 2 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 35 | 1120 |
| 70 and 64 | 2240 |
| 70 and 69 | 4830 |
| 144 and 143 | 20592 |
| 161 and 190 | 30590 |