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 |
|---|---|
| 40 and 153 | 6120 |
| 128 and 53 | 6784 |
| 190 and 156 | 14820 |
| 195 and 193 | 37635 |
| 158 and 83 | 13114 |