Least Common Multiple (LCM) of 75 and 42
The least common multiple (LCM) of 75 and 42 is 1050.
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 75 and 42?
First, calculate the GCD of 75 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 42 = 1 remainder 33 |
| 2 | 42 ÷ 33 = 1 remainder 9 |
| 3 | 33 ÷ 9 = 3 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 60 | 720 |
| 78 and 125 | 9750 |
| 34 and 43 | 1462 |
| 156 and 146 | 11388 |
| 179 and 70 | 12530 |