Least Common Multiple (LCM) of 63 and 189
The least common multiple (LCM) of 63 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 63 and 189?
First, calculate the GCD of 63 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 189 = 0 remainder 63 |
| 2 | 189 ÷ 63 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 73 | 7957 |
| 117 and 112 | 13104 |
| 36 and 182 | 3276 |
| 42 and 54 | 378 |
| 55 and 188 | 10340 |