Least Common Multiple (LCM) of 63 and 107
The least common multiple (LCM) of 63 and 107 is 6741.
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 107?
First, calculate the GCD of 63 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 107 = 0 remainder 63 |
| 2 | 107 ÷ 63 = 1 remainder 44 |
| 3 | 63 ÷ 44 = 1 remainder 19 |
| 4 | 44 ÷ 19 = 2 remainder 6 |
| 5 | 19 ÷ 6 = 3 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 180 | 3060 |
| 175 and 80 | 2800 |
| 133 and 154 | 2926 |
| 136 and 73 | 9928 |
| 107 and 128 | 13696 |