Least Common Multiple (LCM) of 185 and 153
The least common multiple (LCM) of 185 and 153 is 28305.
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 153?
First, calculate the GCD of 185 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 153 = 1 remainder 32 |
| 2 | 153 ÷ 32 = 4 remainder 25 |
| 3 | 32 ÷ 25 = 1 remainder 7 |
| 4 | 25 ÷ 7 = 3 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 186 | 11346 |
| 55 and 70 | 770 |
| 144 and 45 | 720 |
| 161 and 33 | 5313 |
| 105 and 122 | 12810 |