Least Common Multiple (LCM) of 103 and 179
The least common multiple (LCM) of 103 and 179 is 18437.
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 179?
First, calculate the GCD of 103 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 179 = 0 remainder 103 |
| 2 | 179 ÷ 103 = 1 remainder 76 |
| 3 | 103 ÷ 76 = 1 remainder 27 |
| 4 | 76 ÷ 27 = 2 remainder 22 |
| 5 | 27 ÷ 22 = 1 remainder 5 |
| 6 | 22 ÷ 5 = 4 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 35 | 140 |
| 177 and 89 | 15753 |
| 45 and 38 | 1710 |
| 33 and 42 | 462 |
| 122 and 169 | 20618 |