# L.C.M concepts and formula

## L.C.M concepts and formula

One of the most prevalent quantitative aptitude topics asked in government tests is L.C.M. This is one of the most fundamental topics that students are already aware of before they begin studying for competitive exams.

Although the concepts of LCM remain the same, the kind of questions presented in exams may vary. L.C.M is used in all the topic of Quantitative Aptitude, this makes this topic very important.

2-3 word problems related to LCM are asked in exams, but candidates may also expect questions about data sufficiency and data interpretation related to LCM topic.

So, we are providing you with concepts and formulas for the LCM topic to help you prepare properly for the upcoming exams.

When we travel from one point to another, there will be three Quantity that defines this journey – LCM.

#### What is L.C.M (Least Common Multiple)

The least number which is exactly divisible by each one of the given numbers is called their L.C.M

Let’s see an example of L.C.M

Least Common Multiple of 3 and 5

Step-1 List the Multiples of each number,

The multiples of 3 are 3, 6, 9, 12, 15, 18, … etc

The multiples of 5 are 5, 10, 15, 20, 25, … etc

Step-2 Now find the first common value from these multiples this will be the L.C.M.

The first common multiple is 15. So the L.C.M of 3 and 5 is 15.

#### How to calculate the L.C.M.

Let’s find the LCM(10, 12, 15, 75)

Step-1 Write down your numbers in a row

10    12       15       75

Step-2 Divide the layer numbers by a prime number that is evenly divisible into two or more numbers in the layer and bring down the result into the next layer.

Step-3 If any number in the layer is not evenly divisible just bring down that number.

Step-4 Continue dividing layers by prime numbers. When there are no more primes that evenly divided into two or more numbers you are done.

Step-5 The LCM is the product of the numbers in the L shape, left column and bottom row. 1 is ignored.

LCM = 2 × 3 × 5 × 2 × 5
LCM = 300

Therefore, LCM(10, 12, 15, 75) = 300

Q1 Lets find the L.C.M of 12 and 15

Ans

L.C.M of 12 and 15 = 2 x 3 x 2 x 5 = 60

Q2 Find L.C.M of   5, 7, 14, and 20

Ans

L.C.M = 5 x 2 x 7 x 2 = 140

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