Least Common Multiple (LCM) of 134 and 174
The least common multiple (LCM) of 134 and 174 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 134 and 174?
First, calculate the GCD of 134 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 134 ÷ 174 = 0 remainder 134 |
| 2 | 174 ÷ 134 = 1 remainder 40 |
| 3 | 134 ÷ 40 = 3 remainder 14 |
| 4 | 40 ÷ 14 = 2 remainder 12 |
| 5 | 14 ÷ 12 = 1 remainder 2 |
| 6 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 80 | 6960 |
| 174 and 178 | 15486 |
| 89 and 192 | 17088 |
| 32 and 97 | 3104 |
| 181 and 98 | 17738 |