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 |
|---|---|
| 137 and 29 | 3973 |
| 18 and 117 | 234 |
| 158 and 176 | 13904 |
| 109 and 106 | 11554 |
| 187 and 176 | 2992 |