Least Common Multiple (LCM) of 75 and 168
The least common multiple (LCM) of 75 and 168 is 4200.
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 168?
First, calculate the GCD of 75 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 168 = 0 remainder 75 |
| 2 | 168 ÷ 75 = 2 remainder 18 |
| 3 | 75 ÷ 18 = 4 remainder 3 |
| 4 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 68 | 9180 |
| 142 and 62 | 4402 |
| 58 and 200 | 5800 |
| 169 and 174 | 29406 |
| 21 and 10 | 210 |