Least Common Multiple (LCM) of 40 and 171
The least common multiple (LCM) of 40 and 171 is 6840.
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 171?
First, calculate the GCD of 40 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 171 = 0 remainder 40 |
| 2 | 171 ÷ 40 = 4 remainder 11 |
| 3 | 40 ÷ 11 = 3 remainder 7 |
| 4 | 11 ÷ 7 = 1 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 43 | 2322 |
| 100 and 117 | 11700 |
| 114 and 89 | 10146 |
| 72 and 114 | 1368 |
| 155 and 110 | 3410 |