Question

Find HCF of 44,96 and 404 by prime factorisation method. Hence

find their LCM. ​

Answer 1

Given,

The main numbers are = 44,96 and 404

To find,

The HCF or Highest Common Factor of the given numbers, in prime factorization method. And, the LCM or Least Common Multiple of the given numbers.

Solution,

First of all, we will calculate the prime factors of the main numbers by performing the prime factorization.

Prime factorization :

44 = 2 × 2 × 11

96 = 2 x 2 x 2 x 2 x 2 x 3

404 = 2 x 2 x 101

The common factors are = 2,2

The HCF or Highest Common Factor of the given numbers = 2×2 = 4

Now,

LCM or Least Common Multiple of the given numbers =

44 = 2 x 2 x 11 => 2² x 11¹

96 = 2 x 2 x 2 x 2 x 2 x 3 => 2⁵ x 3¹

404 = 2 x 2 x 101 => 2² x 101¹

LCM = 2⁵×3¹×11¹×101¹ = 106656

Hence, the HCF of the main numbers 4 and LCM of the given numbers is 106656.

Answer 2

44=2×2×11

96=2×2×2×2×2×3

404=2×2×101

now,

HCF of 44,96 and 404 is 2×2=4

LCM of 44,96and 404 is 2×2×2×2×2×3×11×101=106656