Least Common Multiple (LCM) of 63 and 109
The least common multiple (LCM) of 63 and 109 is 6867.
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 109?
First, calculate the GCD of 63 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 109 = 0 remainder 63 |
| 2 | 109 ÷ 63 = 1 remainder 46 |
| 3 | 63 ÷ 46 = 1 remainder 17 |
| 4 | 46 ÷ 17 = 2 remainder 12 |
| 5 | 17 ÷ 12 = 1 remainder 5 |
| 6 | 12 ÷ 5 = 2 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 119 | 16779 |
| 126 and 54 | 378 |
| 187 and 104 | 19448 |
| 110 and 70 | 770 |
| 138 and 155 | 21390 |