Least Common Multiple (LCM) of 165 and 100
The least common multiple (LCM) of 165 and 100 is 3300.
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 100?
First, calculate the GCD of 165 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 100 = 1 remainder 65 |
| 2 | 100 ÷ 65 = 1 remainder 35 |
| 3 | 65 ÷ 35 = 1 remainder 30 |
| 4 | 35 ÷ 30 = 1 remainder 5 |
| 5 | 30 ÷ 5 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 145 | 11020 |
| 47 and 47 | 47 |
| 154 and 149 | 22946 |
| 137 and 105 | 14385 |
| 20 and 174 | 1740 |