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 |
|---|---|
| 105 and 83 | 8715 |
| 141 and 18 | 846 |
| 153 and 137 | 20961 |
| 102 and 165 | 5610 |
| 49 and 177 | 8673 |