Least Common Multiple (LCM) of 13 and 178
The least common multiple (LCM) of 13 and 178 is 2314.
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 13 and 178?
First, calculate the GCD of 13 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 178 = 0 remainder 13 |
| 2 | 178 ÷ 13 = 13 remainder 9 |
| 3 | 13 ÷ 9 = 1 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 108 | 864 |
| 118 and 118 | 118 |
| 133 and 155 | 20615 |
| 70 and 78 | 2730 |
| 150 and 169 | 25350 |