Least Common Multiple (LCM) of 105 and 135
The least common multiple (LCM) of 105 and 135 is 945.
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 105 and 135?
First, calculate the GCD of 105 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 135 = 0 remainder 105 |
| 2 | 135 ÷ 105 = 1 remainder 30 |
| 3 | 105 ÷ 30 = 3 remainder 15 |
| 4 | 30 ÷ 15 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 78 | 2262 |
| 174 and 149 | 25926 |
| 137 and 58 | 7946 |
| 26 and 173 | 4498 |
| 144 and 179 | 25776 |