Least Common Multiple (LCM) of 174 and 102
The least common multiple (LCM) of 174 and 102 is 2958.
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 102?
First, calculate the GCD of 174 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 102 = 1 remainder 72 |
| 2 | 102 ÷ 72 = 1 remainder 30 |
| 3 | 72 ÷ 30 = 2 remainder 12 |
| 4 | 30 ÷ 12 = 2 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 171 | 9405 |
| 103 and 172 | 17716 |
| 175 and 131 | 22925 |
| 58 and 180 | 5220 |
| 135 and 78 | 3510 |