Least Common Multiple (LCM) of 21 and 189
The least common multiple (LCM) of 21 and 189 is 189.
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 189?
First, calculate the GCD of 21 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 189 = 0 remainder 21 |
| 2 | 189 ÷ 21 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 63 | 8064 |
| 178 and 116 | 10324 |
| 121 and 131 | 15851 |
| 155 and 66 | 10230 |
| 136 and 148 | 5032 |