Least Common Multiple (LCM) of 126 and 100
The least common multiple (LCM) of 126 and 100 is 6300.
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 100?
First, calculate the GCD of 126 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 100 = 1 remainder 26 |
| 2 | 100 ÷ 26 = 3 remainder 22 |
| 3 | 26 ÷ 22 = 1 remainder 4 |
| 4 | 22 ÷ 4 = 5 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 74 | 3922 |
| 120 and 187 | 22440 |
| 168 and 132 | 1848 |
| 92 and 51 | 4692 |
| 27 and 171 | 513 |