Question

the difference between the LCM and HCF of the number 30 36 and 90 is
a366 b 354 3 186 4 174​

Answer 1

150.

Step-by-step explanation:

Given : Numbers 30,36 and 90.

To find : Difference between the LCM and HCF of the numbers ?

Solution :

First we factories the numbers,

30=2\times 3\times 530=2×3×5

36=2\times 2\times 3\times 336=2×2×3×3

90=2\times 3\times 3\times 590=2×3×3×5

HCF is the highest common factor,

HCF(30,36,90)=2\times 3\times 5HCF(30,36,90)=2×3×5

HCF(30,36,90)=30HCF(30,36,90)=30

LCM is the least common factor,

LCM(30,36,90)=2\times 2\times 3\times 3\times 5LCM(30,36,90)=2×2×3×3×5

LCM(30,36,90)=180LCM(30,36,90)=180

The difference between LCM and HCF is 180-30=150

Therefore, the difference between LCM and HCF of numbers is 150.

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Answer 2

The difference between the LCM and HCF of the number 30 , 36 and 90 is 174 [ The correct option is d. 174 ]

Correct question : The difference between the LCM and HCF of the number 30 , 36 and 90 is a. 366 b. 354 c. 186 d. 174

Given :

The numbers 30 , 36 and 90

To find :

The difference between the LCM and HCF of the number 30 , 36 and 90 is

a. 366

b. 354

c. 186

d. 174

Concept :

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

Relation between HCF and LCM :

HCF × LCM = Product of the numbers

Solution :

Step 1 of 5 :

Write down the given numbers

Here the given numbers are 30 , 36 and 90

Step 2 of 5 :

Prime factorise the given numbers

30 = 2 × 3 × 5

36 = 2 × 2 × 3 × 3

90 = 2 × 3 × 3 × 5

Step 3 of 5 :

Find LCM of 30 , 36 and 90

We know that for the given two or more numbers LCM is the least number which is exactly divisible by each of the given numbers

∴ LCM of 30 , 36 and 90

= 2 × 2 × 3 × 3 × 5

= 180

Step 4 of 5 :

Find HCF of 30 , 36 and 90

We know that for the given two or more numbers HCF is the greatest number that divides each of the numbers

HCF of 30 , 36 and 90

= 2 × 3

= 6

Step 5 of 5 :

Calculate the difference between the LCM and HCF

The difference between the LCM and HCF of the number 30 , 36 and 90

= 180 - 6

= 174

Hence the correct option is d. 174

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