Least Common Multiple (LCM) of 165 and 35
The least common multiple (LCM) of 165 and 35 is 1155.
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 165 and 35?
First, calculate the GCD of 165 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 35 = 4 remainder 25 |
| 2 | 35 ÷ 25 = 1 remainder 10 |
| 3 | 25 ÷ 10 = 2 remainder 5 |
| 4 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 123 | 15621 |
| 75 and 198 | 4950 |
| 199 and 89 | 17711 |
| 162 and 124 | 10044 |
| 116 and 101 | 11716 |