Question

find the HCF of 60 and 84 using prime factorization and LCM of HCF is equal to 6084 and 30​

Answer 1

Step-by-step explanation:

Given find the HCF of 60 and 84 using prime factorization and LCM of HCF is equal to (60,84) and 30  

• We need to find the hcf by using prime factorization of 60 and 84
• So factors of 60 and 84 are
• 60 = 2 x 2 x 3 x 5
• 84 = 2 x 2 x 3 x 7
• So hcf will be 2 x 2 x 3 = 12
• Now we have to find LCM of the hcf obtained and 30.
• So it will be lcm of 12,30
• Factors will be 2 x 3 x 2 x 5 = 60

Reference link will be

https://brainly.in/question/15747606

Answer 2

The HCF of numbers 60 and 84  is 12

The LCM of numbers 30 and HCF of number 60 and 84 i.e LCM of 30 and 12 is 60

Step-by-step explanation:

Given as :

The number are 60 and 84

According to question

Now, HCF of these number using prime factorization

For prime factorization , resolve the given number into prime factors and then find the product of all the prime factor common to all numbers . Then product will give required HCF

So, According to statement

The factor of number 60 = 2 × 2 × 3 × 5

And

The factor of number  84 =  2 × 2 × 3 × 7

So, the highest common factor between numbers = 2 × 2 × 3 = 12

∴  HCF of numbers 60 and 84 = 12

Again

According to question

The LCM of numbers 30 and HCF from number 60 and 84

i.e. The LCM of numbers 30 and 12  using prime factorization

For prime factorization , resolve the given number into prime factors and then find the product of the highest power of all the prime factor that occurs in the resolution of the given numberThen product will give required LCM

So, According to statement

The factor of number 30 = 2 × 3 × 5

And

The factor of number  12 =  2 × 2 × 3

So, the lowest common multiple between numbers =2 × 2 × 3 × 5 = 60

Hence, The HCF of numbers 60 and 84  is 12

And The LCM of numbers 30 and HCF from number 60 and 84 i.e LCM of 30 and 12 is 60  Answer