Least Common Multiple (LCM) of 174 and 32
The least common multiple (LCM) of 174 and 32 is 2784.
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 32?
First, calculate the GCD of 174 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 32 = 5 remainder 14 |
| 2 | 32 ÷ 14 = 2 remainder 4 |
| 3 | 14 ÷ 4 = 3 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 23 | 3680 |
| 30 and 116 | 1740 |
| 117 and 17 | 1989 |
| 78 and 49 | 3822 |
| 197 and 55 | 10835 |