Least Common Multiple (LCM) of 85 and 32
The least common multiple (LCM) of 85 and 32 is 2720.
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 32?
First, calculate the GCD of 85 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 85 ÷ 32 = 2 remainder 21 |
| 2 | 32 ÷ 21 = 1 remainder 11 |
| 3 | 21 ÷ 11 = 1 remainder 10 |
| 4 | 11 ÷ 10 = 1 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 154 | 18942 |
| 172 and 99 | 17028 |
| 176 and 53 | 9328 |
| 32 and 13 | 416 |
| 172 and 195 | 33540 |