Least Common Multiple (LCM) of 116 and 162
The least common multiple (LCM) of 116 and 162 is 9396.
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 162?
First, calculate the GCD of 116 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 162 = 0 remainder 116 |
| 2 | 162 ÷ 116 = 1 remainder 46 |
| 3 | 116 ÷ 46 = 2 remainder 24 |
| 4 | 46 ÷ 24 = 1 remainder 22 |
| 5 | 24 ÷ 22 = 1 remainder 2 |
| 6 | 22 ÷ 2 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 164 | 5412 |
| 31 and 199 | 6169 |
| 17 and 181 | 3077 |
| 117 and 196 | 22932 |
| 134 and 46 | 3082 |