Least Common Multiple (LCM) of 28 and 74
The least common multiple (LCM) of 28 and 74 is 1036.
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 74?
First, calculate the GCD of 28 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 28 ÷ 74 = 0 remainder 28 |
| 2 | 74 ÷ 28 = 2 remainder 18 |
| 3 | 28 ÷ 18 = 1 remainder 10 |
| 4 | 18 ÷ 10 = 1 remainder 8 |
| 5 | 10 ÷ 8 = 1 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 27 | 432 |
| 154 and 150 | 11550 |
| 64 and 117 | 7488 |
| 200 and 175 | 1400 |
| 80 and 88 | 880 |