Least Common Multiple (LCM) of 174 and 140
The least common multiple (LCM) of 174 and 140 is 12180.
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 174 and 140?
First, calculate the GCD of 174 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 140 = 1 remainder 34 |
| 2 | 140 ÷ 34 = 4 remainder 4 |
| 3 | 34 ÷ 4 = 8 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 80 | 2640 |
| 152 and 70 | 5320 |
| 159 and 73 | 11607 |
| 195 and 21 | 1365 |
| 32 and 180 | 1440 |