Least Common Multiple (LCM) of 174 and 189
The least common multiple (LCM) of 174 and 189 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 174 and 189?
First, calculate the GCD of 174 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 189 = 0 remainder 174 |
| 2 | 189 ÷ 174 = 1 remainder 15 |
| 3 | 174 ÷ 15 = 11 remainder 9 |
| 4 | 15 ÷ 9 = 1 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 88 | 264 |
| 138 and 45 | 2070 |
| 85 and 122 | 10370 |
| 145 and 173 | 25085 |
| 76 and 94 | 3572 |