Least Common Multiple (LCM) of 29 and 170
The least common multiple (LCM) of 29 and 170 is 4930.
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 29 and 170?
First, calculate the GCD of 29 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 170 = 0 remainder 29 |
| 2 | 170 ÷ 29 = 5 remainder 25 |
| 3 | 29 ÷ 25 = 1 remainder 4 |
| 4 | 25 ÷ 4 = 6 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 40 | 120 |
| 188 and 67 | 12596 |
| 150 and 46 | 3450 |
| 144 and 31 | 4464 |
| 171 and 102 | 5814 |