Least Common Multiple (LCM) of 126 and 20
The least common multiple (LCM) of 126 and 20 is 1260.
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 20?
First, calculate the GCD of 126 and 20 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 20 = 6 remainder 6 |
| 2 | 20 ÷ 6 = 3 remainder 2 |
| 3 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 60 | 660 |
| 170 and 103 | 17510 |
| 52 and 105 | 5460 |
| 24 and 42 | 168 |
| 145 and 57 | 8265 |