Least Common Multiple (LCM) of 39 and 170
The least common multiple (LCM) of 39 and 170 is 6630.
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 39 and 170?
First, calculate the GCD of 39 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 39 ÷ 170 = 0 remainder 39 |
| 2 | 170 ÷ 39 = 4 remainder 14 |
| 3 | 39 ÷ 14 = 2 remainder 11 |
| 4 | 14 ÷ 11 = 1 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 54 | 1080 |
| 117 and 61 | 7137 |
| 92 and 110 | 5060 |
| 157 and 16 | 2512 |
| 38 and 67 | 2546 |