Least Common Multiple (LCM) of 85 and 72
The least common multiple (LCM) of 85 and 72 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 85 and 72?
First, calculate the GCD of 85 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 72 = 1 remainder 13 |
| 2 | 72 ÷ 13 = 5 remainder 7 |
| 3 | 13 ÷ 7 = 1 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 43 | 3010 |
| 50 and 47 | 2350 |
| 116 and 137 | 15892 |
| 179 and 35 | 6265 |
| 158 and 185 | 29230 |