Least Common Multiple (LCM) of 103 and 68
The least common multiple (LCM) of 103 and 68 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 103 and 68?
First, calculate the GCD of 103 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 68 = 1 remainder 35 |
| 2 | 68 ÷ 35 = 1 remainder 33 |
| 3 | 35 ÷ 33 = 1 remainder 2 |
| 4 | 33 ÷ 2 = 16 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 56 | 616 |
| 70 and 125 | 1750 |
| 127 and 108 | 13716 |
| 80 and 176 | 880 |
| 20 and 74 | 740 |