Least Common Multiple (LCM) of 115 and 162
The least common multiple (LCM) of 115 and 162 is 18630.
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 115 and 162?
First, calculate the GCD of 115 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 162 = 0 remainder 115 |
| 2 | 162 ÷ 115 = 1 remainder 47 |
| 3 | 115 ÷ 47 = 2 remainder 21 |
| 4 | 47 ÷ 21 = 2 remainder 5 |
| 5 | 21 ÷ 5 = 4 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 81 | 12717 |
| 17 and 122 | 2074 |
| 24 and 13 | 312 |
| 111 and 146 | 16206 |
| 116 and 187 | 21692 |