Least Common Multiple (LCM) of 126 and 176
The least common multiple (LCM) of 126 and 176 is 11088.
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 126 and 176?
First, calculate the GCD of 126 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 176 = 0 remainder 126 |
| 2 | 176 ÷ 126 = 1 remainder 50 |
| 3 | 126 ÷ 50 = 2 remainder 26 |
| 4 | 50 ÷ 26 = 1 remainder 24 |
| 5 | 26 ÷ 24 = 1 remainder 2 |
| 6 | 24 ÷ 2 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 194 | 13386 |
| 183 and 101 | 18483 |
| 189 and 171 | 3591 |
| 37 and 17 | 629 |
| 58 and 58 | 58 |