Least Common Multiple (LCM) of 185 and 113
The least common multiple (LCM) of 185 and 113 is 20905.
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 113?
First, calculate the GCD of 185 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 113 = 1 remainder 72 |
| 2 | 113 ÷ 72 = 1 remainder 41 |
| 3 | 72 ÷ 41 = 1 remainder 31 |
| 4 | 41 ÷ 31 = 1 remainder 10 |
| 5 | 31 ÷ 10 = 3 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 152 | 17480 |
| 17 and 158 | 2686 |
| 111 and 54 | 1998 |
| 135 and 199 | 26865 |
| 99 and 173 | 17127 |