Least Common Multiple (LCM) of 40 and 135
The least common multiple (LCM) of 40 and 135 is 1080.
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 40 and 135?
First, calculate the GCD of 40 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 135 = 0 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 |
|---|---|
| 145 and 157 | 22765 |
| 132 and 14 | 924 |
| 18 and 45 | 90 |
| 114 and 166 | 9462 |
| 49 and 18 | 882 |