Least Common Multiple (LCM) of 101 and 187
The least common multiple (LCM) of 101 and 187 is 18887.
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 101 and 187?
First, calculate the GCD of 101 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 187 = 0 remainder 101 |
| 2 | 187 ÷ 101 = 1 remainder 86 |
| 3 | 101 ÷ 86 = 1 remainder 15 |
| 4 | 86 ÷ 15 = 5 remainder 11 |
| 5 | 15 ÷ 11 = 1 remainder 4 |
| 6 | 11 ÷ 4 = 2 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 22 | 4158 |
| 171 and 30 | 1710 |
| 75 and 129 | 3225 |
| 104 and 108 | 2808 |
| 56 and 117 | 6552 |