Least Common Multiple (LCM) of 165 and 74
The least common multiple (LCM) of 165 and 74 is 12210.
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 74?
First, calculate the GCD of 165 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 74 = 2 remainder 17 |
| 2 | 74 ÷ 17 = 4 remainder 6 |
| 3 | 17 ÷ 6 = 2 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 189 | 9450 |
| 180 and 88 | 3960 |
| 42 and 28 | 84 |
| 53 and 176 | 9328 |
| 138 and 27 | 1242 |