Least Common Multiple (LCM) of 180 and 72
The least common multiple (LCM) of 180 and 72 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 180 and 72?
First, calculate the GCD of 180 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 72 = 2 remainder 36 |
| 2 | 72 ÷ 36 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 86 | 8858 |
| 15 and 176 | 2640 |
| 60 and 27 | 540 |
| 120 and 175 | 4200 |
| 165 and 175 | 5775 |