Least Common Multiple (LCM) of 14 and 177
The least common multiple (LCM) of 14 and 177 is 2478.
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 14 and 177?
First, calculate the GCD of 14 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 177 = 0 remainder 14 |
| 2 | 177 ÷ 14 = 12 remainder 9 |
| 3 | 14 ÷ 9 = 1 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 71 | 7952 |
| 101 and 108 | 10908 |
| 149 and 112 | 16688 |
| 174 and 134 | 11658 |
| 173 and 74 | 12802 |