Least Common Multiple (LCM) of 72 and 180
The least common multiple (LCM) of 72 and 180 is 360.
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 180?
First, calculate the GCD of 72 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 180 = 0 remainder 72 |
| 2 | 180 ÷ 72 = 2 remainder 36 |
| 3 | 72 ÷ 36 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 39 | 2184 |
| 107 and 94 | 10058 |
| 152 and 164 | 6232 |
| 189 and 45 | 945 |
| 42 and 176 | 3696 |