Least Common Multiple (LCM) of 174 and 16
The least common multiple (LCM) of 174 and 16 is 1392.
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 16?
First, calculate the GCD of 174 and 16 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 16 = 10 remainder 14 |
| 2 | 16 ÷ 14 = 1 remainder 2 |
| 3 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 25 | 300 |
| 24 and 142 | 1704 |
| 65 and 161 | 10465 |
| 67 and 145 | 9715 |
| 181 and 89 | 16109 |