Least Common Multiple (LCM) of 168 and 75
The least common multiple (LCM) of 168 and 75 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 168 and 75?
First, calculate the GCD of 168 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 75 = 2 remainder 18 |
| 2 | 75 ÷ 18 = 4 remainder 3 |
| 3 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 56 | 1512 |
| 102 and 125 | 12750 |
| 59 and 30 | 1770 |
| 160 and 129 | 20640 |
| 194 and 67 | 12998 |