Least Common Multiple (LCM) of 103 and 162
The least common multiple (LCM) of 103 and 162 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 103 and 162?
First, calculate the GCD of 103 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 162 = 0 remainder 103 |
| 2 | 162 ÷ 103 = 1 remainder 59 |
| 3 | 103 ÷ 59 = 1 remainder 44 |
| 4 | 59 ÷ 44 = 1 remainder 15 |
| 5 | 44 ÷ 15 = 2 remainder 14 |
| 6 | 15 ÷ 14 = 1 remainder 1 |
| 7 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 125 | 20375 |
| 11 and 160 | 1760 |
| 22 and 103 | 2266 |
| 140 and 33 | 4620 |
| 172 and 120 | 5160 |