Least Common Multiple (LCM) of 162 and 193
The least common multiple (LCM) of 162 and 193 is 31266.
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 162 and 193?
First, calculate the GCD of 162 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 162 ÷ 193 = 0 remainder 162 |
| 2 | 193 ÷ 162 = 1 remainder 31 |
| 3 | 162 ÷ 31 = 5 remainder 7 |
| 4 | 31 ÷ 7 = 4 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 48 | 2544 |
| 77 and 116 | 8932 |
| 38 and 38 | 38 |
| 18 and 157 | 2826 |
| 30 and 51 | 510 |