Least Common Multiple (LCM) of 174 and 134
The least common multiple (LCM) of 174 and 134 is 11658.
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 134?
First, calculate the GCD of 174 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 134 = 1 remainder 40 |
| 2 | 134 ÷ 40 = 3 remainder 14 |
| 3 | 40 ÷ 14 = 2 remainder 12 |
| 4 | 14 ÷ 12 = 1 remainder 2 |
| 5 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 114 | 11058 |
| 180 and 36 | 180 |
| 60 and 176 | 2640 |
| 167 and 172 | 28724 |
| 39 and 135 | 1755 |