Least Common Multiple (LCM) of 45 and 135
The least common multiple (LCM) of 45 and 135 is 135.
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 45 and 135?
First, calculate the GCD of 45 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 135 = 0 remainder 45 |
| 2 | 135 ÷ 45 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 79 and 111 | 8769 |
| 155 and 10 | 310 |
| 96 and 132 | 1056 |
| 123 and 17 | 2091 |
| 177 and 187 | 33099 |