Least Common Multiple (LCM) of 117 and 174
The least common multiple (LCM) of 117 and 174 is 6786.
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 117 and 174?
First, calculate the GCD of 117 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 174 = 0 remainder 117 |
| 2 | 174 ÷ 117 = 1 remainder 57 |
| 3 | 117 ÷ 57 = 2 remainder 3 |
| 4 | 57 ÷ 3 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 174 | 174 |
| 11 and 126 | 1386 |
| 101 and 91 | 9191 |
| 151 and 18 | 2718 |
| 68 and 182 | 6188 |