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 |
|---|---|
| 144 and 105 | 5040 |
| 194 and 154 | 14938 |
| 119 and 32 | 3808 |
| 180 and 113 | 20340 |
| 197 and 125 | 24625 |