Least Common Multiple (LCM) of 161 and 113
The least common multiple (LCM) of 161 and 113 is 18193.
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 161 and 113?
First, calculate the GCD of 161 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 161 ÷ 113 = 1 remainder 48 |
| 2 | 113 ÷ 48 = 2 remainder 17 |
| 3 | 48 ÷ 17 = 2 remainder 14 |
| 4 | 17 ÷ 14 = 1 remainder 3 |
| 5 | 14 ÷ 3 = 4 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 104 | 1872 |
| 137 and 48 | 6576 |
| 161 and 197 | 31717 |
| 19 and 96 | 1824 |
| 143 and 138 | 19734 |