Least Common Multiple (LCM) of 185 and 117
The least common multiple (LCM) of 185 and 117 is 21645.
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 117?
First, calculate the GCD of 185 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 117 = 1 remainder 68 |
| 2 | 117 ÷ 68 = 1 remainder 49 |
| 3 | 68 ÷ 49 = 1 remainder 19 |
| 4 | 49 ÷ 19 = 2 remainder 11 |
| 5 | 19 ÷ 11 = 1 remainder 8 |
| 6 | 11 ÷ 8 = 1 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 114 | 5700 |
| 15 and 86 | 1290 |
| 178 and 52 | 4628 |
| 83 and 105 | 8715 |
| 134 and 28 | 1876 |