Least Common Multiple (LCM) of 53 and 187
The least common multiple (LCM) of 53 and 187 is 9911.
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 53 and 187?
First, calculate the GCD of 53 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 187 = 0 remainder 53 |
| 2 | 187 ÷ 53 = 3 remainder 28 |
| 3 | 53 ÷ 28 = 1 remainder 25 |
| 4 | 28 ÷ 25 = 1 remainder 3 |
| 5 | 25 ÷ 3 = 8 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 107 | 11235 |
| 72 and 21 | 504 |
| 43 and 63 | 2709 |
| 96 and 173 | 16608 |
| 155 and 31 | 155 |