Least Common Multiple (LCM) of 103 and 164
The least common multiple (LCM) of 103 and 164 is 16892.
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 164?
First, calculate the GCD of 103 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 164 = 0 remainder 103 |
| 2 | 164 ÷ 103 = 1 remainder 61 |
| 3 | 103 ÷ 61 = 1 remainder 42 |
| 4 | 61 ÷ 42 = 1 remainder 19 |
| 5 | 42 ÷ 19 = 2 remainder 4 |
| 6 | 19 ÷ 4 = 4 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 64 | 1856 |
| 60 and 156 | 780 |
| 19 and 117 | 2223 |
| 45 and 174 | 2610 |
| 133 and 155 | 20615 |