Question

find the HCF and LCM of 12 and 18 by prime factorization method ​

Answer 1

Answer:

HCF

Factors of 12 = 1, 2, 3, 4, 6 and 12.

Factors of 18 = 1, 2, 3, 6, 9 and 18.

Therefore, common factor of 12 and 18 = 1, 2, 3 and 6.

Highest common factor (H.C.F) of 12 and 18 = 6 [since 6 is the highest common factor].

LCM

Find the prime factorization of 12

12 = 2 × 2 × 3

Find the prime factorization of 18

18 = 2 × 3 × 3

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

LCM = 2 × 2 × 3 × 3

LCM = 36

Answer 2

SOLUTION

TO DETERMINE

The HCF and LCM of 12 and 18 by prime factorization method

CONCEPT TO BE IMPLEMENTED

HCF :

For the given two or more numbers HCF is the greatest number that divides each of the numbers

LCM :

For the given two or more numbers LCM is the least number which is exactly divisible by each of the given numbers

EVALUATION

Here the given numbers are 12 and 18

We prime factorise the given numbers

12 = 2 × 2 × 3

18 = 2 × 3 × 3

HCF

= Highest Common Factor

= 2 × 3

= 6

LCM

= 2 × 2 × 3 × 3

= 36

FINAL ANSWER

HCF = 6 , LCM = 36

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