Least Common Multiple (LCM) of 114 and 174
The least common multiple (LCM) of 114 and 174 is 3306.
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 114 and 174?
First, calculate the GCD of 114 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 174 = 0 remainder 114 |
| 2 | 174 ÷ 114 = 1 remainder 60 |
| 3 | 114 ÷ 60 = 1 remainder 54 |
| 4 | 60 ÷ 54 = 1 remainder 6 |
| 5 | 54 ÷ 6 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 25 | 450 |
| 107 and 112 | 11984 |
| 70 and 75 | 1050 |
| 68 and 123 | 8364 |
| 57 and 136 | 7752 |