Least Common Multiple (LCM) of 103 and 106
The least common multiple (LCM) of 103 and 106 is 10918.
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 106?
First, calculate the GCD of 103 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 106 = 0 remainder 103 |
| 2 | 106 ÷ 103 = 1 remainder 3 |
| 3 | 103 ÷ 3 = 34 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 151 | 23707 |
| 75 and 120 | 600 |
| 17 and 18 | 306 |
| 72 and 106 | 3816 |
| 152 and 121 | 18392 |