Least Common Multiple (LCM) of 65 and 170
The least common multiple (LCM) of 65 and 170 is 2210.
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 65 and 170?
First, calculate the GCD of 65 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 170 = 0 remainder 65 |
| 2 | 170 ÷ 65 = 2 remainder 40 |
| 3 | 65 ÷ 40 = 1 remainder 25 |
| 4 | 40 ÷ 25 = 1 remainder 15 |
| 5 | 25 ÷ 15 = 1 remainder 10 |
| 6 | 15 ÷ 10 = 1 remainder 5 |
| 7 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 177 | 15753 |
| 143 and 61 | 8723 |
| 29 and 122 | 3538 |
| 160 and 130 | 2080 |
| 199 and 54 | 10746 |