Least Common Multiple (LCM) of 162 and 103
The least common multiple (LCM) of 162 and 103 is 16686.
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 103?
First, calculate the GCD of 162 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 162 ÷ 103 = 1 remainder 59 |
| 2 | 103 ÷ 59 = 1 remainder 44 |
| 3 | 59 ÷ 44 = 1 remainder 15 |
| 4 | 44 ÷ 15 = 2 remainder 14 |
| 5 | 15 ÷ 14 = 1 remainder 1 |
| 6 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 51 | 1173 |
| 100 and 174 | 8700 |
| 102 and 62 | 3162 |
| 198 and 116 | 11484 |
| 105 and 67 | 7035 |