Least Common Multiple (LCM) of 75 and 174
The least common multiple (LCM) of 75 and 174 is 4350.
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 75 and 174?
First, calculate the GCD of 75 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 174 = 0 remainder 75 |
| 2 | 174 ÷ 75 = 2 remainder 24 |
| 3 | 75 ÷ 24 = 3 remainder 3 |
| 4 | 24 ÷ 3 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 45 | 360 |
| 42 and 144 | 1008 |
| 102 and 75 | 2550 |
| 159 and 58 | 9222 |
| 158 and 144 | 11376 |