Least Common Multiple (LCM) of 175 and 45
The least common multiple (LCM) of 175 and 45 is 1575.
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 175 and 45?
First, calculate the GCD of 175 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 45 = 3 remainder 40 |
| 2 | 45 ÷ 40 = 1 remainder 5 |
| 3 | 40 ÷ 5 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 121 | 13673 |
| 51 and 186 | 3162 |
| 30 and 109 | 3270 |
| 110 and 162 | 8910 |
| 103 and 141 | 14523 |