Least Common Multiple (LCM) of 72 and 85
The least common multiple (LCM) of 72 and 85 is 6120.
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 85?
First, calculate the GCD of 72 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 85 = 0 remainder 72 |
| 2 | 85 ÷ 72 = 1 remainder 13 |
| 3 | 72 ÷ 13 = 5 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 181 | 7240 |
| 120 and 82 | 4920 |
| 25 and 135 | 675 |
| 54 and 126 | 378 |
| 85 and 147 | 12495 |