Least Common Multiple (LCM) of 22 and 170
The least common multiple (LCM) of 22 and 170 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 170?
First, calculate the GCD of 22 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 22 ÷ 170 = 0 remainder 22 |
| 2 | 170 ÷ 22 = 7 remainder 16 |
| 3 | 22 ÷ 16 = 1 remainder 6 |
| 4 | 16 ÷ 6 = 2 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 14 | 1526 |
| 157 and 117 | 18369 |
| 144 and 178 | 12816 |
| 36 and 175 | 6300 |
| 41 and 82 | 82 |