Least Common Multiple (LCM) of 68 and 103
The least common multiple (LCM) of 68 and 103 is 7004.
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 68 and 103?
First, calculate the GCD of 68 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 103 = 0 remainder 68 |
| 2 | 103 ÷ 68 = 1 remainder 35 |
| 3 | 68 ÷ 35 = 1 remainder 33 |
| 4 | 35 ÷ 33 = 1 remainder 2 |
| 5 | 33 ÷ 2 = 16 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 128 | 10880 |
| 123 and 91 | 11193 |
| 99 and 122 | 12078 |
| 79 and 106 | 8374 |
| 186 and 94 | 8742 |