Least Common Multiple (LCM) of 126 and 40
The least common multiple (LCM) of 126 and 40 is 2520.
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 40?
First, calculate the GCD of 126 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 40 = 3 remainder 6 |
| 2 | 40 ÷ 6 = 6 remainder 4 |
| 3 | 6 ÷ 4 = 1 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 84 | 2100 |
| 134 and 34 | 2278 |
| 136 and 123 | 16728 |
| 134 and 134 | 134 |
| 82 and 38 | 1558 |