The hcf and lcm of two numbers are 12 and 720. how many such pair(s) of numbers are possible

Last updated - May 03, 2022

Answer: HCF = 12 and LCM = 720

Step by step solution:

Contents:

Given numbers = 12 and 720

To find HCF and LCM by prime factorization method, first we will find prime factors of given numbers.

Prime Factorization of 12:
12 = 2 × 6
= 2 × 2 × 3

Prime Factorization of 720:

HCF of 12 and 720 by prime factorization method:

Common factors in above prime factors of given numbers are underlined.

Common prime factors = 2, 2, 3

Now we have to multiply these common prime factors to obtain the HCF of given numbers.

HCF = 2 × 2 × 3
= 12

∴ HCF(12, 720) = 12

LCM of 12 and 720 by prime factorization method:

Now to find the LCM we will note down how many times the each factor has occurred in above prime factors of given numbers.

In above table we have also noted the maximum occurrence of the each factor in the prime factors of the given numbers.

Now to obtain the LCM of given numbers we will multiply each factor maximum number of times it occurred in above table.

LCM = 2 × 2 × 2 × 2 × 3 × 3 × 5
= 720

∴ LCM(12, 720) = 720

Division Method:

HCF of 12 and 720 by division method:

In the above division, the last divisor is 12.

Hence the HCF(GCD) of 12 and 720 = 12

∴ HCF(12, 720) = 12

LCM of 12 and 720 by division method

∴ LCM(12, 720) = 720

If the HCF of two numbers is 12 and their product is 8640, what is their LCM?

If the LCM of two numbers is 720 and their product is 8640, what is their HCF?

HCF and LCM of two numbers is 12 and 720 respectively. If one number is 12, what is the other number?

Let other number be x.
Given:
HCF(12, x) = 12
LCM(12, x) = 720
∵ HCF × LCM = product of numbers
∴ 12 × 720 = 12 × x
∴ 8640 = 12x
∴ 8640⁄12 = x
∴ x = 720
Hence, the other number is 720.