Least Common Multiple (LCM) of 174 and 38
The least common multiple (LCM) of 174 and 38 is 3306.
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 38?
First, calculate the GCD of 174 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 38 = 4 remainder 22 |
| 2 | 38 ÷ 22 = 1 remainder 16 |
| 3 | 22 ÷ 16 = 1 remainder 6 |
| 4 | 16 ÷ 6 = 2 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 42 | 7098 |
| 133 and 189 | 3591 |
| 95 and 28 | 2660 |
| 52 and 153 | 7956 |
| 32 and 115 | 3680 |