Least Common Multiple (LCM) of 185 and 168
The least common multiple (LCM) of 185 and 168 is 31080.
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 185 and 168?
First, calculate the GCD of 185 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 168 = 1 remainder 17 |
| 2 | 168 ÷ 17 = 9 remainder 15 |
| 3 | 17 ÷ 15 = 1 remainder 2 |
| 4 | 15 ÷ 2 = 7 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 46 | 3450 |
| 21 and 112 | 336 |
| 93 and 119 | 11067 |
| 54 and 18 | 54 |
| 42 and 101 | 4242 |