Least Common Multiple (LCM) of 28 and 67
The least common multiple (LCM) of 28 and 67 is 1876.
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 28 and 67?
First, calculate the GCD of 28 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 28 ÷ 67 = 0 remainder 28 |
| 2 | 67 ÷ 28 = 2 remainder 11 |
| 3 | 28 ÷ 11 = 2 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 33 | 5775 |
| 112 and 140 | 560 |
| 169 and 199 | 33631 |
| 97 and 62 | 6014 |
| 134 and 120 | 8040 |