Least Common Multiple (LCM) of 72 and 45
The least common multiple (LCM) of 72 and 45 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 45?
First, calculate the GCD of 72 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 45 = 1 remainder 27 |
| 2 | 45 ÷ 27 = 1 remainder 18 |
| 3 | 27 ÷ 18 = 1 remainder 9 |
| 4 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 85 | 510 |
| 146 and 39 | 5694 |
| 102 and 132 | 2244 |
| 161 and 77 | 1771 |
| 31 and 99 | 3069 |