Question

The pairs of numbers 3,5 and 1, 15 have

(a) same HCF but different LCM
(b) different HCF but same LCM
(c) different HCF and different LCM
(d) same HCF and same LCM​

Answer 1

Answer:

(d) same hcf and same lcm

Answer 2

Given,

Number pairs are = I) 3,5 and II) 1,15

To find,

Relationship between the LCM and HCF of the given number pairs.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

LCM of the given pairs,

First pair :

3 and 5 are prime numbers, so their LCM will be their product.

LCM = 3×5 = 15

Second Pair :

Multiples of 1 = 1,2,3,4....,14,15...

Multiples of 15 = 15,30,45....

Thus, LCM = 15

HCF of the given pairs :

First pair

3 and 5 are prime numbers. And, HCF of two prime number is always 1.

HCF = 1

Second pair,

Factors of 1 = 1

Factors of 15 = 1,3,5

Common factor = 1

HCF = 1

So, Their LCM are equal, and HCF are also equal.

Hence, they have same HCF and same LCM. (option D)