Least Common Multiple (LCM) of 187 and 135
The least common multiple (LCM) of 187 and 135 is 25245.
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 187 and 135?
First, calculate the GCD of 187 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 187 ÷ 135 = 1 remainder 52 |
| 2 | 135 ÷ 52 = 2 remainder 31 |
| 3 | 52 ÷ 31 = 1 remainder 21 |
| 4 | 31 ÷ 21 = 1 remainder 10 |
| 5 | 21 ÷ 10 = 2 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 67 | 5360 |
| 54 and 145 | 7830 |
| 192 and 83 | 15936 |
| 126 and 98 | 882 |
| 198 and 87 | 5742 |