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 |
|---|---|
| 161 and 104 | 16744 |
| 35 and 143 | 5005 |
| 113 and 174 | 19662 |
| 54 and 73 | 3942 |
| 181 and 95 | 17195 |