Least Common Multiple (LCM) of 165 and 75
The least common multiple (LCM) of 165 and 75 is 825.
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 75?
First, calculate the GCD of 165 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 75 = 2 remainder 15 |
| 2 | 75 ÷ 15 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 40 | 6520 |
| 148 and 72 | 2664 |
| 56 and 90 | 2520 |
| 129 and 141 | 6063 |
| 192 and 37 | 7104 |