Least Common Multiple (LCM) of 174 and 45
The least common multiple (LCM) of 174 and 45 is 2610.
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 45?
First, calculate the GCD of 174 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 45 = 3 remainder 39 |
| 2 | 45 ÷ 39 = 1 remainder 6 |
| 3 | 39 ÷ 6 = 6 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 88 and 80 | 880 |
| 147 and 34 | 4998 |
| 199 and 190 | 37810 |
| 33 and 18 | 198 |
| 153 and 87 | 4437 |