Least Common Multiple (LCM) of 127 and 174
The least common multiple (LCM) of 127 and 174 is 22098.
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 127 and 174?
First, calculate the GCD of 127 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 174 = 0 remainder 127 |
| 2 | 174 ÷ 127 = 1 remainder 47 |
| 3 | 127 ÷ 47 = 2 remainder 33 |
| 4 | 47 ÷ 33 = 1 remainder 14 |
| 5 | 33 ÷ 14 = 2 remainder 5 |
| 6 | 14 ÷ 5 = 2 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 88 | 440 |
| 78 and 75 | 1950 |
| 75 and 81 | 2025 |
| 183 and 193 | 35319 |
| 180 and 36 | 180 |