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 |
|---|---|
| 142 and 61 | 8662 |
| 135 and 123 | 5535 |
| 143 and 109 | 15587 |
| 12 and 13 | 156 |
| 63 and 33 | 693 |