Least Common Multiple (LCM) of 100 and 126
The least common multiple (LCM) of 100 and 126 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 100 and 126?
First, calculate the GCD of 100 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 126 = 0 remainder 100 |
| 2 | 126 ÷ 100 = 1 remainder 26 |
| 3 | 100 ÷ 26 = 3 remainder 22 |
| 4 | 26 ÷ 22 = 1 remainder 4 |
| 5 | 22 ÷ 4 = 5 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 36 | 1332 |
| 85 and 125 | 2125 |
| 100 and 176 | 4400 |
| 172 and 197 | 33884 |
| 195 and 195 | 195 |