Least Common Multiple (LCM) of 104 and 67
The least common multiple (LCM) of 104 and 67 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 104 and 67?
First, calculate the GCD of 104 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 67 = 1 remainder 37 |
| 2 | 67 ÷ 37 = 1 remainder 30 |
| 3 | 37 ÷ 30 = 1 remainder 7 |
| 4 | 30 ÷ 7 = 4 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 14 | 1694 |
| 147 and 144 | 7056 |
| 152 and 20 | 760 |
| 34 and 59 | 2006 |
| 112 and 76 | 2128 |