Least Common Multiple (LCM) of 30 and 174
The least common multiple (LCM) of 30 and 174 is 870.
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 30 and 174?
First, calculate the GCD of 30 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 174 = 0 remainder 30 |
| 2 | 174 ÷ 30 = 5 remainder 24 |
| 3 | 30 ÷ 24 = 1 remainder 6 |
| 4 | 24 ÷ 6 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 150 | 4200 |
| 49 and 149 | 7301 |
| 190 and 123 | 23370 |
| 50 and 189 | 9450 |
| 71 and 157 | 11147 |