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 |
|---|---|
| 100 and 114 | 5700 |
| 111 and 128 | 14208 |
| 26 and 173 | 4498 |
| 76 and 170 | 6460 |
| 101 and 119 | 12019 |