Least Common Multiple (LCM) of 22 and 85
The least common multiple (LCM) of 22 and 85 is 1870.
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 22 and 85?
First, calculate the GCD of 22 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 22 ÷ 85 = 0 remainder 22 |
| 2 | 85 ÷ 22 = 3 remainder 19 |
| 3 | 22 ÷ 19 = 1 remainder 3 |
| 4 | 19 ÷ 3 = 6 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 160 | 160 |
| 87 and 127 | 11049 |
| 88 and 198 | 792 |
| 138 and 91 | 12558 |
| 44 and 80 | 880 |