Least Common Multiple (LCM) of 103 and 66
The least common multiple (LCM) of 103 and 66 is 6798.
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 103 and 66?
First, calculate the GCD of 103 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 66 = 1 remainder 37 |
| 2 | 66 ÷ 37 = 1 remainder 29 |
| 3 | 37 ÷ 29 = 1 remainder 8 |
| 4 | 29 ÷ 8 = 3 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 72 | 3096 |
| 41 and 154 | 6314 |
| 33 and 167 | 5511 |
| 37 and 140 | 5180 |
| 53 and 51 | 2703 |