Least Common Multiple (LCM) of 13 and 174
The least common multiple (LCM) of 13 and 174 is 2262.
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 174?
First, calculate the GCD of 13 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 174 = 0 remainder 13 |
| 2 | 174 ÷ 13 = 13 remainder 5 |
| 3 | 13 ÷ 5 = 2 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 168 | 4872 |
| 90 and 62 | 2790 |
| 180 and 75 | 900 |
| 78 and 45 | 1170 |
| 82 and 116 | 4756 |