Least Common Multiple (LCM) of 106 and 63
The least common multiple (LCM) of 106 and 63 is 6678.
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 106 and 63?
First, calculate the GCD of 106 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 63 = 1 remainder 43 |
| 2 | 63 ÷ 43 = 1 remainder 20 |
| 3 | 43 ÷ 20 = 2 remainder 3 |
| 4 | 20 ÷ 3 = 6 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 92 | 1840 |
| 107 and 35 | 3745 |
| 52 and 66 | 1716 |
| 42 and 134 | 2814 |
| 101 and 31 | 3131 |