Question

find the H. C. F and l. c. m of the number 15,19,and25​

Answer 1

Answer:

Step-by-step explanation:

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).

We need to calculate greatest common factor 15 and 19, than apply into the LCM equation.

GCF(15,19) = 1

LCM(15,19) = ( 15 × 19) / 1

LCM(15,19) = 285 / 1

LCM(15,19) = 285

Least Common Multiple (LCM) of 15 and 19 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 15 and 19. First we will calculate the prime factors of 15 and 19.

Prime Factorization of 15

Prime factors of 15 are 3, 5. Prime factorization of 15 in exponential form is:

15 = 31 × 51

Prime Factorization of 19

Prime factors of 19 are 19. Prime factorization of 19 in exponential form is:

19 = 191

Now multiplying the highest exponent prime factors to calculate the LCM of 15 and 19.

LCM(15,19) = 31 × 51 × 191

LCM(15,19) = 285

Answer 2

answer

We will learn the relationship between H.C.F. and L.C.M. of two numbers.

First we need to find the highest common factor (H.C.F.) of 15 and 18 which is 3.

Then we need to find the lowest common multiple (L.C.M.) of 15 and 18 which is 90.

H.C.F. × L.C.M. = 3 × 90 = 270

Also the product of numbers = 15 × 18 = 270

Therefore, product of H.C.F. and L.C.M. of 15 and 18 = product of 15 and 18.

Again, let us consider the two numbers 16 and 24

Prime factors of 16 and 24 are:

16 = 2 × 2 × 2 × 2

24 = 2 × 2 × 2 × 3

L.C.M. of 16 and 24 is 48;

H.C.F. of 16 and 24 is 8;

L.C.M. × H.C.F. = 48 × 8 = 384

Product of numbers = 16 × 24 = 384

So, from the above explanations we conclude that the product of highest common factor (H.C.F.) and lowest common multiple (L.C.M.) of two numbers is equal to the product of two numbers

or, H.C.F. × L.C.M. = First number × Second number

or, L.C.M. = First Number×Second NumberH.C.F.

or, L.C.M. × H.C.F. = Product of two given numbers

or, L.C.M. = Product of Two Given NumbersH.C.F.

or, H.C.F. = Product of Two Given NumbersL.C.M.