Least Common Multiple (LCM) of 174 and 78
The least common multiple (LCM) of 174 and 78 is 2262.
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 174 and 78?
First, calculate the GCD of 174 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 78 = 2 remainder 18 |
| 2 | 78 ÷ 18 = 4 remainder 6 |
| 3 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 150 | 4800 |
| 189 and 83 | 15687 |
| 199 and 125 | 24875 |
| 76 and 81 | 6156 |
| 96 and 108 | 864 |