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 |
|---|---|
| 147 and 53 | 7791 |
| 172 and 148 | 6364 |
| 72 and 149 | 10728 |
| 194 and 107 | 20758 |
| 147 and 108 | 5292 |