Least Common Multiple (LCM) of 135 and 175
The least common multiple (LCM) of 135 and 175 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 135 and 175?
First, calculate the GCD of 135 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 175 = 0 remainder 135 |
| 2 | 175 ÷ 135 = 1 remainder 40 |
| 3 | 135 ÷ 40 = 3 remainder 15 |
| 4 | 40 ÷ 15 = 2 remainder 10 |
| 5 | 15 ÷ 10 = 1 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 167 | 11523 |
| 47 and 183 | 8601 |
| 58 and 35 | 2030 |
| 194 and 115 | 22310 |
| 128 and 117 | 14976 |