Least Common Multiple (LCM) of 145 and 75
The least common multiple (LCM) of 145 and 75 is 2175.
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 145 and 75?
First, calculate the GCD of 145 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 75 = 1 remainder 70 |
| 2 | 75 ÷ 70 = 1 remainder 5 |
| 3 | 70 ÷ 5 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 172 | 7740 |
| 133 and 167 | 22211 |
| 189 and 54 | 378 |
| 181 and 93 | 16833 |
| 183 and 14 | 2562 |