Least Common Multiple (LCM) of 23 and 170
The least common multiple (LCM) of 23 and 170 is 3910.
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 23 and 170?
First, calculate the GCD of 23 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 170 = 0 remainder 23 |
| 2 | 170 ÷ 23 = 7 remainder 9 |
| 3 | 23 ÷ 9 = 2 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 64 | 5056 |
| 93 and 186 | 186 |
| 160 and 95 | 3040 |
| 105 and 122 | 12810 |
| 37 and 58 | 2146 |