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 |
|---|---|
| 124 and 147 | 18228 |
| 162 and 198 | 1782 |
| 183 and 132 | 8052 |
| 130 and 112 | 7280 |
| 172 and 159 | 27348 |