Question

The LCM of two numbers is 210 and their HCF is 14. How many such pairs are possible​

Answer 1

Step-by-step explanation:

first divide

210 /14

formula LCM / HCF

15 Answar

Answer 2

Two pairs (14 , 210) and (42 , 70) are possible

Given :

The LCM of two numbers is 210 and their HCF is 14.

To find :

The number of such possible pairs

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 2 :

Form the equation to find number of possible pairs

Here it is given that LCM of two numbers is 210 and their HCF is 14.

Let the numbers are 14m and 14n where m and n are co-primes

HCF × LCM = Product of the numbers

⇒ 210 × 14 = 14m × 14n

Step 2 of 2 :

Find number of possible pairs

210 × 14 = 14m × 14n

⇒ 14m × 14n = 210 × 14

⇒ m × n = 210/14

⇒ m × n = 15

Since m and n are co-primes

∴ m = 1 , n = 15 and m = 3 , n = 5

So possible pairs are (14 , 210) and (42 , 70)

Hence two pairs (14 , 210) and (42 , 70) are possible

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