Least Common Multiple (LCM) of 36 and 170
The least common multiple (LCM) of 36 and 170 is 3060.
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 36 and 170?
First, calculate the GCD of 36 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 170 = 0 remainder 36 |
| 2 | 170 ÷ 36 = 4 remainder 26 |
| 3 | 36 ÷ 26 = 1 remainder 10 |
| 4 | 26 ÷ 10 = 2 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 182 | 5824 |
| 50 and 89 | 4450 |
| 20 and 180 | 180 |
| 180 and 145 | 5220 |
| 85 and 182 | 15470 |