Least Common Multiple (LCM) of 63 and 87
The least common multiple (LCM) of 63 and 87 is 1827.
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 87?
First, calculate the GCD of 63 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 87 = 0 remainder 63 |
| 2 | 87 ÷ 63 = 1 remainder 24 |
| 3 | 63 ÷ 24 = 2 remainder 15 |
| 4 | 24 ÷ 15 = 1 remainder 9 |
| 5 | 15 ÷ 9 = 1 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 200 | 6600 |
| 175 and 19 | 3325 |
| 156 and 197 | 30732 |
| 167 and 13 | 2171 |
| 147 and 109 | 16023 |