Least Common Multiple (LCM) of 72 and 135
The least common multiple (LCM) of 72 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 72 and 135?
First, calculate the GCD of 72 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 135 = 0 remainder 72 |
| 2 | 135 ÷ 72 = 1 remainder 63 |
| 3 | 72 ÷ 63 = 1 remainder 9 |
| 4 | 63 ÷ 9 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 115 | 3105 |
| 181 and 28 | 5068 |
| 189 and 18 | 378 |
| 152 and 197 | 29944 |
| 36 and 32 | 288 |