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 |
|---|---|
| 31 and 85 | 2635 |
| 166 and 113 | 18758 |
| 176 and 114 | 10032 |
| 176 and 53 | 9328 |
| 95 and 45 | 855 |