Least Common Multiple (LCM) of 189 and 174
The least common multiple (LCM) of 189 and 174 is 10962.
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 189 and 174?
First, calculate the GCD of 189 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 174 = 1 remainder 15 |
| 2 | 174 ÷ 15 = 11 remainder 9 |
| 3 | 15 ÷ 9 = 1 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 90 | 3870 |
| 114 and 103 | 11742 |
| 200 and 177 | 35400 |
| 30 and 183 | 1830 |
| 25 and 163 | 4075 |