Least Common Multiple (LCM) of 104 and 126
The least common multiple (LCM) of 104 and 126 is 6552.
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 104 and 126?
First, calculate the GCD of 104 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 126 = 0 remainder 104 |
| 2 | 126 ÷ 104 = 1 remainder 22 |
| 3 | 104 ÷ 22 = 4 remainder 16 |
| 4 | 22 ÷ 16 = 1 remainder 6 |
| 5 | 16 ÷ 6 = 2 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 40 | 360 |
| 127 and 55 | 6985 |
| 17 and 37 | 629 |
| 163 and 33 | 5379 |
| 196 and 154 | 2156 |