Least Common Multiple (LCM) of 175 and 135
The least common multiple (LCM) of 175 and 135 is 4725.
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 135?
First, calculate the GCD of 175 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 135 = 1 remainder 40 |
| 2 | 135 ÷ 40 = 3 remainder 15 |
| 3 | 40 ÷ 15 = 2 remainder 10 |
| 4 | 15 ÷ 10 = 1 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 112 | 1680 |
| 132 and 179 | 23628 |
| 46 and 155 | 7130 |
| 180 and 27 | 540 |
| 21 and 192 | 1344 |