Least Common Multiple (LCM) of 96 and 174
The least common multiple (LCM) of 96 and 174 is 2784.
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 96 and 174?
First, calculate the GCD of 96 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 174 = 0 remainder 96 |
| 2 | 174 ÷ 96 = 1 remainder 78 |
| 3 | 96 ÷ 78 = 1 remainder 18 |
| 4 | 78 ÷ 18 = 4 remainder 6 |
| 5 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 98 | 6762 |
| 41 and 114 | 4674 |
| 41 and 194 | 7954 |
| 29 and 49 | 1421 |
| 137 and 200 | 27400 |