Least Common Multiple (LCM) of 52 and 170
The least common multiple (LCM) of 52 and 170 is 4420.
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 52 and 170?
First, calculate the GCD of 52 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 170 = 0 remainder 52 |
| 2 | 170 ÷ 52 = 3 remainder 14 |
| 3 | 52 ÷ 14 = 3 remainder 10 |
| 4 | 14 ÷ 10 = 1 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 110 | 10120 |
| 144 and 39 | 1872 |
| 158 and 57 | 9006 |
| 111 and 61 | 6771 |
| 86 and 84 | 3612 |