Least Common Multiple (LCM) of 108 and 63
The least common multiple (LCM) of 108 and 63 is 756.
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 108 and 63?
First, calculate the GCD of 108 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 63 = 1 remainder 45 |
| 2 | 63 ÷ 45 = 1 remainder 18 |
| 3 | 45 ÷ 18 = 2 remainder 9 |
| 4 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 51 | 9588 |
| 63 and 136 | 8568 |
| 111 and 34 | 3774 |
| 199 and 98 | 19502 |
| 165 and 69 | 3795 |