Least Common Multiple (LCM) of 68 and 104
The least common multiple (LCM) of 68 and 104 is 1768.
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 104?
First, calculate the GCD of 68 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 104 = 0 remainder 68 |
| 2 | 104 ÷ 68 = 1 remainder 36 |
| 3 | 68 ÷ 36 = 1 remainder 32 |
| 4 | 36 ÷ 32 = 1 remainder 4 |
| 5 | 32 ÷ 4 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 65 | 260 |
| 111 and 145 | 16095 |
| 117 and 103 | 12051 |
| 68 and 141 | 9588 |
| 130 and 115 | 2990 |