Question

If P is a prime number then
what is the LCM of P P2 P3​

Answer 1

Answer:-
If P is a prime number then LCM of P1,P2 and P3 will be :-

LCM(P1,P2,P3) = P1xP2xP3

Explanation:-

WHAT IS LCM?

LCM stands for Lowest Common Multiple.

It is the common multiple of two or more than two numbers .

The smallest number which is multiple of two/more numbers is said to be LCM.

e.g. LCM of 10 and 15 is 30.

HOW TO CALCULATE LCM?

LCM can be easily calculated by prime factorisation method as described below.

1. Two no. 15 and 10

2. To find its LCM we will factorise them as follows

10 = 2 x 5

15 = 3 x 5

3.Now, we will multiply the unique multiples from both the numbers while the repeated factor only once.

N.B. Always take the maximum degree if any factor get repeat.

LCM(10,15) = 2 x 3 x 5 = 30

Similarly

LCM (3,18) is 18 itself as;

3 = 1x 3

18 = 3^2 x 2

LCM(3,18) = 3^2 x 2 = 18 (ans)

LCM OF PRIME NUMBERS :-

What is Prime number?

A number which has only two factors i.e. 1 and the number itself are known as prime factors . e.g. 2,3,5,7,11,13,17,19 etc.

N.B. 1 is neither prime nor composite number. and composite numbers has more than one factor like 4,6,8,9,10,12etc.

THE PRIME FACTORISATION OF PRIMENUMBERS RESULTS IN 1 AND NUMBER ITSELF.

Hence,

LCM(Prime numbers) = Product of numbers

i.e. LCM(P1,P2,P3) = P1xP2xP3

e.g. LCM(3,5) = 3 x 5 = 15

as, 3 = 1 x 3

     5 = 1x 5

LCM ( 3,7,11) = 3 x 7 x 11 = 231