Least Common Multiple (LCM) of 67 and 104
The least common multiple (LCM) of 67 and 104 is 6968.
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 67 and 104?
First, calculate the GCD of 67 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 104 = 0 remainder 67 |
| 2 | 104 ÷ 67 = 1 remainder 37 |
| 3 | 67 ÷ 37 = 1 remainder 30 |
| 4 | 37 ÷ 30 = 1 remainder 7 |
| 5 | 30 ÷ 7 = 4 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 15 | 2130 |
| 191 and 15 | 2865 |
| 173 and 94 | 16262 |
| 120 and 59 | 7080 |
| 118 and 35 | 4130 |