Least Common Multiple (LCM) of 101 and 126
The least common multiple (LCM) of 101 and 126 is 12726.
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 101 and 126?
First, calculate the GCD of 101 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 126 = 0 remainder 101 |
| 2 | 126 ÷ 101 = 1 remainder 25 |
| 3 | 101 ÷ 25 = 4 remainder 1 |
| 4 | 25 ÷ 1 = 25 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 18 | 126 |
| 11 and 53 | 583 |
| 161 and 97 | 15617 |
| 21 and 60 | 420 |
| 190 and 74 | 7030 |