Least Common Multiple (LCM) of 174 and 68
The least common multiple (LCM) of 174 and 68 is 5916.
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 68?
First, calculate the GCD of 174 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 68 = 2 remainder 38 |
| 2 | 68 ÷ 38 = 1 remainder 30 |
| 3 | 38 ÷ 30 = 1 remainder 8 |
| 4 | 30 ÷ 8 = 3 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 182 | 26390 |
| 110 and 120 | 1320 |
| 172 and 159 | 27348 |
| 198 and 99 | 198 |
| 176 and 73 | 12848 |