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 |
|---|---|
| 154 and 19 | 2926 |
| 182 and 18 | 1638 |
| 186 and 105 | 6510 |
| 21 and 71 | 1491 |
| 165 and 28 | 4620 |