Least Common Multiple (LCM) of 64 and 165
The least common multiple (LCM) of 64 and 165 is 10560.
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 64 and 165?
First, calculate the GCD of 64 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 165 = 0 remainder 64 |
| 2 | 165 ÷ 64 = 2 remainder 37 |
| 3 | 64 ÷ 37 = 1 remainder 27 |
| 4 | 37 ÷ 27 = 1 remainder 10 |
| 5 | 27 ÷ 10 = 2 remainder 7 |
| 6 | 10 ÷ 7 = 1 remainder 3 |
| 7 | 7 ÷ 3 = 2 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 171 | 2394 |
| 65 and 51 | 3315 |
| 66 and 185 | 12210 |
| 149 and 87 | 12963 |
| 99 and 133 | 13167 |