Least Common Multiple (LCM) of 18 and 174
The least common multiple (LCM) of 18 and 174 is 522.
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 18 and 174?
First, calculate the GCD of 18 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 18 ÷ 174 = 0 remainder 18 |
| 2 | 174 ÷ 18 = 9 remainder 12 |
| 3 | 18 ÷ 12 = 1 remainder 6 |
| 4 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 172 | 9116 |
| 163 and 53 | 8639 |
| 152 and 110 | 8360 |
| 50 and 45 | 450 |
| 190 and 90 | 1710 |