Least Common Multiple (LCM) of 185 and 42
The least common multiple (LCM) of 185 and 42 is 7770.
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 42?
First, calculate the GCD of 185 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 42 = 4 remainder 17 |
| 2 | 42 ÷ 17 = 2 remainder 8 |
| 3 | 17 ÷ 8 = 2 remainder 1 |
| 4 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 104 | 2184 |
| 199 and 71 | 14129 |
| 20 and 137 | 2740 |
| 100 and 97 | 9700 |
| 96 and 180 | 1440 |