Least Common Multiple (LCM) of 135 and 72
The least common multiple (LCM) of 135 and 72 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 135 and 72?
First, calculate the GCD of 135 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 72 = 1 remainder 63 |
| 2 | 72 ÷ 63 = 1 remainder 9 |
| 3 | 63 ÷ 9 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 165 | 30360 |
| 181 and 170 | 30770 |
| 15 and 23 | 345 |
| 103 and 76 | 7828 |
| 112 and 38 | 2128 |