Least Common Multiple (LCM) of 40 and 47
The least common multiple (LCM) of 40 and 47 is 1880.
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 47?
First, calculate the GCD of 40 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 47 = 0 remainder 40 |
| 2 | 47 ÷ 40 = 1 remainder 7 |
| 3 | 40 ÷ 7 = 5 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 91 and 190 | 17290 |
| 110 and 177 | 19470 |
| 135 and 54 | 270 |
| 160 and 42 | 3360 |
| 91 and 98 | 1274 |