Least Common Multiple (LCM) of 65 and 167
The least common multiple (LCM) of 65 and 167 is 10855.
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 167?
First, calculate the GCD of 65 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 167 = 0 remainder 65 |
| 2 | 167 ÷ 65 = 2 remainder 37 |
| 3 | 65 ÷ 37 = 1 remainder 28 |
| 4 | 37 ÷ 28 = 1 remainder 9 |
| 5 | 28 ÷ 9 = 3 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 63 | 2520 |
| 28 and 21 | 84 |
| 66 and 144 | 1584 |
| 105 and 142 | 14910 |
| 198 and 51 | 3366 |