Least Common Multiple (LCM) of 40 and 126
The least common multiple (LCM) of 40 and 126 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 40 and 126?
First, calculate the GCD of 40 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 126 = 0 remainder 40 |
| 2 | 126 ÷ 40 = 3 remainder 6 |
| 3 | 40 ÷ 6 = 6 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 88 and 118 | 5192 |
| 194 and 68 | 6596 |
| 130 and 141 | 18330 |
| 40 and 142 | 2840 |
| 90 and 27 | 270 |