This blog notes down all key concepts to remember to be able to use the GMAT Least Common Multiple and Highest Common Factor for problem-solving. Many GMAT Data Sufficiency problems will need the know-how of the number properties so we can infer if sufficient information is available or not.

**L**east Common Multiple Definition

LCM stands for least common multiple for a set of numbers. This is the **smallest number which is divisible by each number in the set. **To compute the LCM for a set of numbers, we can follow the following steps. *e.g. We will take numbers 12 and 30 and try to find their LCM.*

**Prime Factorise**: The first step would be to prime factorise all the numbers in the set.*The prime factors for 12 and 30 are:*- 12 = (2)^2 * (3)
- 30 = (2)*(3)*(5)

**Highest Power:**Now we take the**maxima of the highest power**for each of the prime factors.*We have 3 prime factors: 2, 3, 5.***LCM = (2)^2*(3)*(5) = 60**

**Highest Common Factor Definition**

The HCF aka the **highest common factor **stands for the common factor for a set of numbers. **This is the largest number that divides all numbers in the set.** To compute the HCF, we can follow the following steps. e.g. *We will take numbers 12 and 30 and try to find their HCF.*

**Prime Factorise**: The first step would be to prime factorise all the numbers in the set.*The prime factors for 12 and 30 are:*- 12 = (2)^2 * (3)
- 30 = (2)*(3)*(5)

**Lowest Power:**Now we take the**minima of the power**s for each of the prime factors.*We have 3 prime factors: 2, 3, 5.**We take the common powers for the factors. The lowest power for 5 is 0.***HCF = (2)*(3)*(5)^0 =**6

The common factor is thereby 6 here.

To be continued …