Least Common Multiple (LCM) & Highest Common Factor (HCF) are the two most popular topics on which questions appear in all major competitive exams. LCM and HCF are easy concepts to understand so questions from these areas can be solved in less time.

LCM of two or more numbers is the least number which is divisible by the given numbers.

The HCF, also known as Greatest Common Divisor (GCD), of two or more numbers is the highest number that can divide the given numbers.

Example 1: What is the LCM of 8 and 12?

Multiples of 8 are: 8, 16, 24, 32, 40, 48, …

Multiples of 12 are: 12, 18, 24, 36, 48, …

Common multiples of 8 and 12 are simply the numbers that are part of both sequences, and these are:

24, 48, …

So, from this list of the first few common multiples of the numbers 8 and 12, their least common multiple is 24.

Example 2: What is the HCF of 8 and 12?

Factors of 8 are: 1, 2, 4, 8

Factors of 12 are: 1, 2, 3, 4, 6, 12

Common factors of 8 and 12 are simply the numbers that are part of both sequence, and these are:

1, 2, 4

So, from this list of the common factors of the numbers 8 and 12, their HCF or GCD is 4.

Following are competitive exams in which questions are asked from LCM and HCF:

MBA: CAT, XAT, IIFT, SNAP, TISSNET, MAT, MICAT, CMAT, ATMA,GMAT

Government Exams: UPSC-CSE, SSC, BANK-PO, RRB, CDS, RBI-Grade B etc.

BBA: IP-MAT, NPAT, DU-JAT, IPU-CET, SET

LAW: CLAT, AILET, SET, IPU-CET, MAH-CET

Others: GRE, SAT etc.