Least Common Multiple (LCM) of 107 and 63
The least common multiple (LCM) of 107 and 63 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 107 and 63?
First, calculate the GCD of 107 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 63 = 1 remainder 44 |
| 2 | 63 ÷ 44 = 1 remainder 19 |
| 3 | 44 ÷ 19 = 2 remainder 6 |
| 4 | 19 ÷ 6 = 3 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 41 | 1845 |
| 78 and 12 | 156 |
| 173 and 161 | 27853 |
| 123 and 26 | 3198 |
| 111 and 119 | 13209 |