Least Common Multiple (LCM) of 21 and 187
The least common multiple (LCM) of 21 and 187 is 3927.
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 21 and 187?
First, calculate the GCD of 21 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 187 = 0 remainder 21 |
| 2 | 187 ÷ 21 = 8 remainder 19 |
| 3 | 21 ÷ 19 = 1 remainder 2 |
| 4 | 19 ÷ 2 = 9 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 75 | 600 |
| 173 and 145 | 25085 |
| 42 and 54 | 378 |
| 194 and 30 | 2910 |
| 108 and 19 | 2052 |