Least Common Multiple (LCM) of 18 and 175
The least common multiple (LCM) of 18 and 175 is 3150.
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 175?
First, calculate the GCD of 18 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 18 ÷ 175 = 0 remainder 18 |
| 2 | 175 ÷ 18 = 9 remainder 13 |
| 3 | 18 ÷ 13 = 1 remainder 5 |
| 4 | 13 ÷ 5 = 2 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 16 | 240 |
| 178 and 148 | 13172 |
| 45 and 112 | 5040 |
| 170 and 70 | 1190 |
| 85 and 23 | 1955 |