Least Common Multiple (LCM) of 40 and 71
The least common multiple (LCM) of 40 and 71 is 2840.
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 71?
First, calculate the GCD of 40 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 71 = 0 remainder 40 |
| 2 | 71 ÷ 40 = 1 remainder 31 |
| 3 | 40 ÷ 31 = 1 remainder 9 |
| 4 | 31 ÷ 9 = 3 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 17 | 2822 |
| 196 and 31 | 6076 |
| 172 and 56 | 2408 |
| 90 and 96 | 1440 |
| 84 and 85 | 7140 |