Least Common Multiple (LCM) of 135 and 170
The least common multiple (LCM) of 135 and 170 is 4590.
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 170?
First, calculate the GCD of 135 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 170 = 0 remainder 135 |
| 2 | 170 ÷ 135 = 1 remainder 35 |
| 3 | 135 ÷ 35 = 3 remainder 30 |
| 4 | 35 ÷ 30 = 1 remainder 5 |
| 5 | 30 ÷ 5 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 177 | 1770 |
| 161 and 120 | 19320 |
| 116 and 151 | 17516 |
| 73 and 15 | 1095 |
| 82 and 82 | 82 |