Least Common Multiple (LCM) of 116 and 161
The least common multiple (LCM) of 116 and 161 is 18676.
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 116 and 161?
First, calculate the GCD of 116 and 161 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 161 = 0 remainder 116 |
| 2 | 161 ÷ 116 = 1 remainder 45 |
| 3 | 116 ÷ 45 = 2 remainder 26 |
| 4 | 45 ÷ 26 = 1 remainder 19 |
| 5 | 26 ÷ 19 = 1 remainder 7 |
| 6 | 19 ÷ 7 = 2 remainder 5 |
| 7 | 7 ÷ 5 = 1 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 174 | 17574 |
| 165 and 152 | 25080 |
| 78 and 84 | 1092 |
| 62 and 191 | 11842 |
| 190 and 193 | 36670 |