Least Common Multiple (LCM) of 126 and 178
The least common multiple (LCM) of 126 and 178 is 11214.
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 178?
First, calculate the GCD of 126 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 178 = 0 remainder 126 |
| 2 | 178 ÷ 126 = 1 remainder 52 |
| 3 | 126 ÷ 52 = 2 remainder 22 |
| 4 | 52 ÷ 22 = 2 remainder 8 |
| 5 | 22 ÷ 8 = 2 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 106 | 3498 |
| 118 and 36 | 2124 |
| 137 and 35 | 4795 |
| 141 and 149 | 21009 |
| 183 and 162 | 9882 |