Least Common Multiple (LCM) of 40 and 174
The least common multiple (LCM) of 40 and 174 is 3480.
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 174?
First, calculate the GCD of 40 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 174 = 0 remainder 40 |
| 2 | 174 ÷ 40 = 4 remainder 14 |
| 3 | 40 ÷ 14 = 2 remainder 12 |
| 4 | 14 ÷ 12 = 1 remainder 2 |
| 5 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 99 | 14058 |
| 149 and 91 | 13559 |
| 177 and 16 | 2832 |
| 54 and 145 | 7830 |
| 30 and 24 | 120 |